diff --git a/stdlib/map.ml b/stdlib/map.ml
index 54eaf4fe8..b5d9a08ca 100644
--- a/stdlib/map.ml
+++ b/stdlib/map.ml
@@ -270,12 +270,13 @@ module Make(Ord: OrderedType) = struct
 
     let rec filter p = function
         Empty -> Empty
-      | Node(l, v, d, r, _) ->
+      | Node(l, v, d, r, _) as t ->
           (* call [p] in the expected left-to-right order *)
           let l' = filter p l in
           let pvd = p v d in
           let r' = filter p r in
-          if pvd then join l' v d r' else concat l' r'
+          if pvd then if l==l' && r==r' then t else join l' v d r'
+          else concat l' r'
 
     let rec partition p = function
         Empty -> (Empty, Empty)
diff --git a/stdlib/map.mli b/stdlib/map.mli
index b97a43b54..4a6ced5c8 100644
--- a/stdlib/map.mli
+++ b/stdlib/map.mli
@@ -134,7 +134,9 @@ module type S =
 
     val filter: (key -> 'a -> bool) -> 'a t -> 'a t
     (** [filter p m] returns the map with all the bindings in [m]
-        that satisfy predicate [p].
+        that satisfy predicate [p]. If [p] satisfies every binding in [m],
+        [m] is returned unchanged (the result of the function is then
+        physically equal to [m])
         @since 3.12.0
      *)
 
diff --git a/testsuite/tests/lib-set/testmap.ml b/testsuite/tests/lib-set/testmap.ml
index 5d5972bc8..8792ae7f0 100644
--- a/testsuite/tests/lib-set/testmap.ml
+++ b/testsuite/tests/lib-set/testmap.ml
@@ -147,3 +147,11 @@ let () =
 
   assert (!m2 == !m1);
   assert(a2 -. a1 = a1 -. a0)
+
+let () =
+  (* check that filtering a map where all bindings are satisfied by
+     the given predicate returns the original map *)
+  let m1 = ref M.empty in
+  for i = 1 to 10 do m1 := M.add i (float i) !m1 done;
+  let m2 = M.filter (fun e _ -> e >= 0) !m1 in
+  assert (m2 == !m1)