diff --git a/src/msgspec/_json_schema.py b/src/msgspec/_json_schema.py
index 650cf1b8..b88f2b20 100644
--- a/src/msgspec/_json_schema.py
+++ b/src/msgspec/_json_schema.py
@@ -330,7 +330,6 @@ def to_schema(self, t: mi.Type, check_ref: bool = True) -> dict[str, Any]:
         elif isinstance(t, mi.UnionType):
             structs = {}
             other = []
-            has_none = False
             none_member = None
             tag_field = None
             for subtype in t.types:
@@ -341,7 +340,6 @@ def to_schema(self, t: mi.Type, check_ref: bool = True) -> dict[str, Any]:
                     tag_field = real_type.tag_field
                     structs[real_type.tag] = real_type
                 elif isinstance(real_type, mi.NoneType):
-                    has_none = True
                     none_member = subtype
                 else:
                     other.append(subtype)
@@ -359,21 +357,21 @@ def to_schema(self, t: mi.Type, check_ref: bool = True) -> dict[str, Any]:
                 }
                 if options:
                     options.append(struct_schema)
-                    if has_none:
+                    if none_member is not None:
                         options.append(self.to_schema(none_member))
                     schema["anyOf"] = options
-                elif has_none:
+                elif none_member is not None:
                     schema["anyOf"] = [struct_schema, self.to_schema(none_member)]
                 else:
                     schema.update(struct_schema)
             elif len(structs) == 1:
                 _, subtype = structs.popitem()
                 options.append(self.to_schema(subtype))
-                if has_none:
+                if none_member is not None:
                     options.append(self.to_schema(none_member))
                 schema["anyOf"] = options
             else:
-                if has_none:
+                if none_member is not None:
                     options.append(self.to_schema(none_member))
                 schema["anyOf"] = options
         elif isinstance(t, mi.LiteralType):