diff --git a/Lib/inspect.py b/Lib/inspect.py
index d06c8078ded870..af2943454832f2 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -2486,29 +2486,11 @@ def _signature_from_callable(obj, *,
         else:
             return sig
 
-    # Was this function wrapped by a decorator?
-    if follow_wrapper_chains:
-        # Unwrap until we find an explicit signature or a MethodType (which will be
-        # handled explicitly below).
-        obj = unwrap(obj, stop=(lambda f: hasattr(f, "__signature__")
-                                or isinstance(f, types.MethodType)))
-        if isinstance(obj, types.MethodType):
-            # If the unwrapped object is a *method*, we might want to
-            # skip its first parameter (self).
-            # See test_signature_wrapped_bound_method for details.
-            return _get_signature_of(obj)
-
-    try:
-        sig = obj.__signature__
-    except AttributeError:
-        pass
-    else:
-        if sig is not None:
-            if not isinstance(sig, Signature):
-                raise TypeError(
-                    'unexpected object {!r} in __signature__ '
-                    'attribute'.format(sig))
-            return sig
+    # See issue 44337, handle functools.partial and functools.partialmethod
+    # before follow_wrapper_chains.
+    if isinstance(obj, functools.partial):
+        wrapped_sig = _get_signature_of(obj.func)
+        return _signature_get_partial(wrapped_sig, obj)
 
     try:
         partialmethod = obj.__partialmethod__
@@ -2543,9 +2525,29 @@ def _signature_from_callable(obj, *,
                 new_params = (first_wrapped_param,) + sig_params
                 return sig.replace(parameters=new_params)
 
-    if isinstance(obj, functools.partial):
-        wrapped_sig = _get_signature_of(obj.func)
-        return _signature_get_partial(wrapped_sig, obj)
+    # Was this function wrapped by a decorator?
+    if follow_wrapper_chains:
+        # Unwrap until we find an explicit signature or a MethodType (which will be
+        # handled explicitly below).
+        obj = unwrap(obj, stop=(lambda f: hasattr(f, "__signature__")
+                                or isinstance(f, types.MethodType)))
+        if isinstance(obj, types.MethodType):
+            # If the unwrapped object is a *method*, we might want to
+            # skip its first parameter (self).
+            # See test_signature_wrapped_bound_method for details.
+            return _get_signature_of(obj)
+
+    try:
+        sig = obj.__signature__
+    except AttributeError:
+        pass
+    else:
+        if sig is not None:
+            if not isinstance(sig, Signature):
+                raise TypeError(
+                    'unexpected object {!r} in __signature__ '
+                    'attribute'.format(sig))
+            return sig
 
     if isfunction(obj) or _signature_is_functionlike(obj):
         # If it's a pure Python function, or an object that is duck type
diff --git a/Lib/test/test_inspect/test_inspect.py b/Lib/test/test_inspect/test_inspect.py
index c5581041f044b1..e52a41ff37d018 100644
--- a/Lib/test/test_inspect/test_inspect.py
+++ b/Lib/test/test_inspect/test_inspect.py
@@ -4087,6 +4087,30 @@ def foo(a): pass
         foo.__partialmethod__ = 'spam'
         self.assertEqual(str(inspect.signature(foo)), '(a)')
 
+    def test_signature_on_partial_unchange_in_update_wrapper(self):
+        from functools import partial, update_wrapper
+
+        def test(a, b, c, d):
+            pass
+        p = partial(test, a=1)
+        sig_partial = inspect.signature(p)
+        update_wrapper(p, test)
+        sig_updated = inspect.signature(p)
+        self.assertEqual(sig_updated, sig_partial)
+
+    def test_signature_on_partial_method_unchange_in_update_wrapper(self):
+        from functools import partialmethod, update_wrapper
+
+        class Spam:
+            def test(it, a, b, c, d) -> 'spam':
+                pass
+            ham = partialmethod(test, a=1)
+
+        sig_partial = inspect.signature(Spam.ham)
+        update_wrapper(Spam.ham, Spam.test)
+        sig_updated = inspect.signature(Spam.ham)
+        self.assertEqual(sig_updated, sig_partial)
+
     def test_signature_on_decorated(self):
         def decorator(func):
             @functools.wraps(func)
diff --git a/Misc/NEWS.d/next/Library/2022-03-07-05-38-20.bpo-46761.4mt4cJ.rst b/Misc/NEWS.d/next/Library/2022-03-07-05-38-20.bpo-46761.4mt4cJ.rst
new file mode 100644
index 00000000000000..dc138949339e52
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-03-07-05-38-20.bpo-46761.4mt4cJ.rst
@@ -0,0 +1 @@
+Make :func:`inspect.signature()` returns correct signature after :func:`functools.update_wrapper()` is called. Patch by Ofey Chan.