diff --git a/mathics/builtin/assignments/clear.py b/mathics/builtin/assignments/clear.py
index b31bbae06..0777b699a 100644
--- a/mathics/builtin/assignments/clear.py
+++ b/mathics/builtin/assignments/clear.py
@@ -17,18 +17,13 @@
 )
 from mathics.core.builtin import Builtin, PostfixOperator
 from mathics.core.expression import Expression
-from mathics.core.symbols import Atom, Symbol, SymbolNull, symbol_set
+from mathics.core.symbols import Atom, Symbol, SymbolNull
 from mathics.core.systemsymbols import (
+    SYSTEM_SYMBOL_VALUES,
     SymbolContext,
     SymbolContextPath,
-    SymbolDownValues,
     SymbolFailed,
-    SymbolMessages,
-    SymbolNValues,
     SymbolOptions,
-    SymbolOwnValues,
-    SymbolSubValues,
-    SymbolUpValues,
 )
 
 
@@ -258,7 +253,6 @@ class Unset(PostfixOperator):
 
     def eval(self, expr, evaluation):
         "Unset[expr_]"
-
         head = expr.get_head()
         if head in SYSTEM_SYMBOL_VALUES:
             if len(expr.elements) != 1:
@@ -284,13 +278,11 @@ def eval(self, expr, evaluation):
                 return SymbolFailed
         return SymbolNull
 
-
-SYSTEM_SYMBOL_VALUES = symbol_set(
-    SymbolDownValues,
-    SymbolMessages,
-    SymbolNValues,
-    SymbolOptions,
-    SymbolOwnValues,
-    SymbolSubValues,
-    SymbolUpValues,
-)
+    def eval_unset_makeboxes(self, expr, evaluation):
+        "Unset[expr:MakeBoxes[_, _]]"
+        if not evaluation.definitions.unset_format(
+            "System`MakeBoxes", "_MakeBoxes", expr
+        ):
+            evaluation.message("Unset", "norep", expr, Symbol("System`MakeBoxes"))
+            return SymbolFailed
+        return SymbolNull
diff --git a/mathics/builtin/forms/print.py b/mathics/builtin/forms/print.py
index 685a16d54..ce5a1d406 100644
--- a/mathics/builtin/forms/print.py
+++ b/mathics/builtin/forms/print.py
@@ -19,6 +19,7 @@
 from mathics.core.expression import Expression
 from mathics.core.symbols import SymbolFalse, SymbolTrue
 from mathics.core.systemsymbols import SymbolInputForm, SymbolOutputForm
+from mathics.format.box.formatvalues import do_format_element
 from mathics.format.box.makeboxes import is_print_form_callback
 from mathics.format.form import render_input_form, render_output_form
 
@@ -256,8 +257,8 @@ def eval_makeboxes_outputform(expr: BaseElement, evaluation: Evaluation, **kwarg
     """
     Build a 2D representation of the expression using only keyboard characters.
     """
-
-    text_outputform = str(render_output_form(expr, evaluation, **kwargs))
+    f_expr = do_format_element(expr, evaluation, SymbolOutputForm)
+    text_outputform = str(render_output_form(f_expr, evaluation, **kwargs))
     pane = PaneBox(String('"' + text_outputform + '"'))
     return InterpretationBox(
         pane, Expression(SymbolOutputForm, expr), **{"System`Editable": SymbolFalse}
diff --git a/mathics/core/assignment.py b/mathics/core/assignment.py
index f25dec5eb..d273518c7 100644
--- a/mathics/core/assignment.py
+++ b/mathics/core/assignment.py
@@ -115,13 +115,22 @@ def get_symbol_values(
     except KeyError:
         return ListExpression()
 
-    elements = []
+    elements: list[BaseElement] = []
 
     if position == "formatvalues":
         format_rules = definition.formatvalues
         for key, rules in format_rules.items():
-            if key == "System`MakeBoxes":
-                elements.extend(rules)
+            if key == "_MakeBoxes":
+                elements.extend(
+                    (
+                        Expression(
+                            SymbolRuleDelayed,
+                            Expression(SymbolHoldPattern, rule.pattern.expr),
+                            rule.replace,
+                        )
+                        for rule in rules
+                    )
+                )
                 continue
             if key:
                 elements.extend(
diff --git a/mathics/core/definitions.py b/mathics/core/definitions.py
index 46624b2e6..3059d6081 100644
--- a/mathics/core/definitions.py
+++ b/mathics/core/definitions.py
@@ -107,6 +107,15 @@ def add_rule(self, rule: BaseRule) -> bool:
             return self.add_rule_at(rule, pos)
         return False
 
+    def remove_format_rule(self, lhs: BaseElement, form: str) -> bool:
+        """Remove a rule"""
+        format_rule_list = self.formatvalues.get(form, [])
+        for index, existing in enumerate(format_rule_list):
+            if existing.pattern.expr.sameQ(lhs):
+                del format_rule_list[index]
+                return True
+        return False
+
     def remove_rule(self, lhs: BaseElement) -> bool:
         """Remove a rule"""
         position = get_tag_position(lhs, self.name)
@@ -810,6 +819,15 @@ def unset(self, name: str, expr: BaseElement) -> bool:
         self.clear_definitions_cache(name)
         return result
 
+    def unset_format(self, name: str, form: str, expr: BaseElement) -> bool:
+        """Remove the rule corresponding to the expression `expr` in
+        the format `form` of the Definition `name`"""
+        definition = self.get_user_definition(self.lookup_name(name))
+        result = definition.remove_format_rule(expr, form)
+        self.mark_changed(definition)
+        self.clear_definitions_cache(name)
+        return result
+
     def get_config_value(
         self, name: str, default: Optional[int] = None
     ) -> Optional[int]:
diff --git a/mathics/core/systemsymbols.py b/mathics/core/systemsymbols.py
index 234bf694d..cfbd92b87 100644
--- a/mathics/core/systemsymbols.py
+++ b/mathics/core/systemsymbols.py
@@ -447,3 +447,13 @@
     SymbolRepeated,
     SymbolRepeatedNull,
 )
+
+SYSTEM_SYMBOL_VALUES = symbol_set(
+    SymbolDownValues,
+    SymbolMessages,
+    SymbolNValues,
+    SymbolOptions,
+    SymbolOwnValues,
+    SymbolSubValues,
+    SymbolUpValues,
+)
diff --git a/mathics/format/box/formatvalues.py b/mathics/format/box/formatvalues.py
index 90210bcfd..37ea3c2d1 100644
--- a/mathics/format/box/formatvalues.py
+++ b/mathics/format/box/formatvalues.py
@@ -30,7 +30,7 @@
     SymbolRepeatedNull,
     SymbolTimes,
 )
-from mathics.core.systemsymbols import SymbolMinus
+from mathics.core.systemsymbols import SymbolInputForm, SymbolMinus, SymbolOutputForm
 
 # These Strings are used in Boxing output
 StringElipsis = String("...")
@@ -74,12 +74,18 @@ def do_format_element(
         head = element.get_head()  # use element.head
         elements = element.get_elements()
         include_form = False
-        # If the expression is enclosed by a Format
-        # takes the form from the expression and
-        # removes the format from the expression.
-        if head in OUTPUT_FORMS and len(elements) == 1 and isinstance(head, Symbol):
-            expr = elements[0]
-            if not form.sameQ(head):
+
+        if elements is not None and len(elements) == 1:
+            # Special cases: SymbolInputForm and SymbolOutputForm
+            # are only processed from MakeBoxes, using the explicit
+            # form parameter.
+            if head in (SymbolInputForm, SymbolOutputForm):
+                return expr
+            # If the expression is enclosed by other Format
+            # takes the form from the expression and
+            # removes the format from the expression.
+            if head in OUTPUT_FORMS and isinstance(head, Symbol):
+                expr = elements[0]
                 form = head
                 include_form = True
 
diff --git a/mathics/format/box/makeboxes.py b/mathics/format/box/makeboxes.py
index 38c7a01c0..5d0f1ad81 100644
--- a/mathics/format/box/makeboxes.py
+++ b/mathics/format/box/makeboxes.py
@@ -26,6 +26,8 @@
 from mathics.core.systemsymbols import (  # SymbolRule, SymbolRuleDelayed,
     SymbolAborted,
     SymbolComplex,
+    SymbolInputForm,
+    SymbolOutputForm,
     SymbolParentForm,
     SymbolRational,
     SymbolStandardForm,
@@ -332,7 +334,12 @@ def format_element(
     """
     was_boxing = evaluation.is_boxing
     evaluation.is_boxing = True
-    formatted_expr = do_format(element, evaluation, form)
+    # InputForm and OutputForm do format in the MakeBoxes implementation.
+    if form in (SymbolInputForm, SymbolOutputForm):
+        formatted_expr = element
+    else:
+        formatted_expr = do_format(element, evaluation, form)
+
     if form not in evaluation.definitions.boxforms:
         formatted_expr = Expression(form, formatted_expr)
         form = SymbolStandardForm
diff --git a/mathics/format/form/inputform.py b/mathics/format/form/inputform.py
index 80c8f5e6d..b25dfc8ad 100644
--- a/mathics/format/form/inputform.py
+++ b/mathics/format/form/inputform.py
@@ -197,6 +197,15 @@ def _infix_expression_to_inputform_text(
     return result
 
 
+@register_inputform("System`OutputForm")
+def outputform(expr: Expression, evaluation: Evaluation, **kwargs):
+    from .outputform import render_output_form
+
+    if len(expr.elements) != 1:
+        raise _WrongFormattedExpression
+    return render_output_form(expr.elements[0], evaluation, **kwargs)
+
+
 @register_inputform("System`Prefix")
 def _prefix_expression_to_inputform_text(
     expr: Expression, evaluation: Evaluation, **kwargs
diff --git a/mathics/format/form/outputform.py b/mathics/format/form/outputform.py
index 3e6d3774e..5a94d37fe 100644
--- a/mathics/format/form/outputform.py
+++ b/mathics/format/form/outputform.py
@@ -442,7 +442,9 @@ def _infix_outputform_text(expr: Expression, evaluation: Evaluation, **kwargs) -
 
 @register_outputform("System`InputForm")
 def inputform(expr: Expression, evaluation: Evaluation, **kwargs):
-    return render_input_form(expr, evaluation, **kwargs)
+    if len(expr.elements) != 1:
+        raise _WrongFormattedExpression
+    return render_input_form(expr.elements[0], evaluation, **kwargs)
 
 
 @register_outputform("System`List")
diff --git a/test/format/test_makeboxes.py b/test/format/test_makeboxes.py
index 6969d3854..1626df519 100644
--- a/test/format/test_makeboxes.py
+++ b/test/format/test_makeboxes.py
@@ -172,6 +172,7 @@ def test_makeboxes_others_fail(str_expr, str_expected, msg):
 @pytest.mark.parametrize(
     ("str_expr", "str_expected", "msg"),
     [
+        (None, None, None),
         (
             r"MakeBoxes[G[F[2.]], StandardForm]",
             r'RowBox[{"G","[",RowBox[{"F","[","2.`","]"}],"]"}]',
@@ -199,7 +200,7 @@ def test_makeboxes_others_fail(str_expr, str_expected, msg):
         ),
         (
             r"MakeBoxes[OutputForm[G[F[3.002]]], StandardForm]",
-            r'InterpretationBox[PaneBox["\"G[{Formatted f, {3.002}, Standard}]\""], G[{Formatted f, {3.002}, Standard}], Editable -> False]',
+            r'InterpretationBox[PaneBox["\"G[{Formatted f, {3.002}, Standard}]\""], OutputForm[G[F[3.002]]], Editable -> False]',
             "with the defined OutputForm",
         ),
         (
@@ -215,7 +216,7 @@ def test_makeboxes_others_fail(str_expr, str_expected, msg):
         # InterpretationBox is now used here... = InterpretationBox[PaneBox["\"G[{Formatted f, {3.002}, Output}]\""], OutputForm[G[F[3.002`]]], Rule[Editable, False]]
         (
             r"MakeBoxes[OutputForm[G[F[3.002]]], StandardForm]",
-            r'RowBox[{"G","[",RowBox[{"{",RowBox[{"\"Formatted f\"",", ",RowBox[{"{","3.002","}"}],", ","\"Standard\""}],"}"}],"]"}]',
+            r'InterpretationBox[PaneBox["\"G[{Formatted f, {3.002}, Output}]\""], OutputForm[G[F[3.002]]], Rule[Editable, False]]',
             "Test Custom OutputForm",
         ),
         (
@@ -225,8 +226,8 @@ def test_makeboxes_others_fail(str_expr, str_expected, msg):
         ),
         (
             r"MakeBoxes[F[x_], fmt_]=.; MakeBoxes[G[F[2.]], StandardForm]",
-            r'RowBox[{"G","[",RowBox[{"F","[","2.","]"}],"]"}]',
-            "Clear MakeBoxes rule",
+            r'RowBox[{"G", "[", RowBox[{"F", "[", "2.`", "]"}], "]"}]',
+            "Clear MakeBoxes rule - Fails because <<MakeBoxes[F[x_], fmt_]>> does not clear the rule.",
         ),
     ],
 )
@@ -260,6 +261,7 @@ def test_makeboxes_custom(str_expr, str_expected, msg):
 @pytest.mark.parametrize(
     ("str_expr", "str_expected", "msg"),
     [
+        (None, None, None),
         (
             r'MakeBoxes[F[x__], fmt_] :=  RowBox[{"F", "<~", RowBox[MakeBoxes[#1, fmt] & /@ List[x]], "~>"}]',
             "Null",