diff --git a/docs/misc/changelog.rst b/docs/misc/changelog.rst
index 4cff7277f..8f08ccca4 100644
--- a/docs/misc/changelog.rst
+++ b/docs/misc/changelog.rst
@@ -4,7 +4,7 @@ Changelog
 ==========
 
 
-Release 2.1.0a3 (WIP)
+Release 2.1.0a4 (WIP)
 --------------------------
 
 Breaking Changes:
@@ -27,7 +27,8 @@ Bug Fixes:
 ^^^^^^^^^^
 - Relaxed check in logger, that was causing issue on Windows with colorama
 - Fixed off-policy algorithms with continuous float64 actions (see #1145) (@tobirohrer)
-
+- Fixed env_checker.py warning messages for out of bounds in complex observation spaces (@Gabo-Tor)
+ 
 Deprecations:
 ^^^^^^^^^^^^^
 
@@ -1398,7 +1399,7 @@ And all the contributors:
 @eleurent @ac-93 @cove9988 @theDebugger811 @hsuehch @Demetrio92 @thomasgubler @IperGiove @ScheiklP
 @simoninithomas @armandpl @manuel-delverme @Gautam-J @gianlucadecola @buoyancy99 @caburu @xy9485
 @Gregwar @ycheng517 @quantitative-technologies @bcollazo @git-thor @TibiGG @cool-RR @MWeltevrede
-@carlosluis @arjun-kg @tlpss @JonathanKuelz
+@carlosluis @arjun-kg @tlpss @JonathanKuelz @Gabo-Tor
 @Melanol @qgallouedec @francescoluciano @jlp-ue @burakdmb @timothe-chaumont @honglu2875
 @anand-bala @hughperkins @sidney-tio @AlexPasqua @dominicgkerr @Akhilez @Rocamonde @tobirohrer @ZikangXiong
 @DavyMorgan @luizapozzobon @Bonifatius94 @theSquaredError @harveybellini @DavyMorgan @FieteO @jonasreiher @npit @WeberSamuel @troiganto
diff --git a/stable_baselines3/common/env_checker.py b/stable_baselines3/common/env_checker.py
index 516d7ba61..8b8da7f44 100644
--- a/stable_baselines3/common/env_checker.py
+++ b/stable_baselines3/common/env_checker.py
@@ -203,18 +203,24 @@ def _check_obs(obs: Union[tuple, dict, np.ndarray, int], observation_space: spac
             f"Expected: {observation_space.dtype}, actual dtype: {obs.dtype}"
         )
         if isinstance(observation_space, spaces.Box):
-            assert np.all(obs >= observation_space.low), (
-                f"The observation returned by the `{method_name}()` method does not match the lower bound "
-                f"of the given observation space {observation_space}."
-                f"Expected: obs >= {np.min(observation_space.low)}, "
-                f"actual min value: {np.min(obs)} at index {np.argmin(obs)}"
-            )
-            assert np.all(obs <= observation_space.high), (
-                f"The observation returned by the `{method_name}()` method does not match the upper bound "
-                f"of the given observation space {observation_space}. "
-                f"Expected: obs <= {np.max(observation_space.high)}, "
-                f"actual max value: {np.max(obs)} at index {np.argmax(obs)}"
-            )
+            lower_bounds, upper_bounds = observation_space.low, observation_space.high
+            # Expose all invalid indices at once
+            invalid_indices = np.where(np.logical_or(obs < lower_bounds, obs > upper_bounds))
+            if (obs > upper_bounds).any() or (obs < lower_bounds).any():
+                message = (
+                    f"The observation returned by the `{method_name}()` method does not match the bounds "
+                    f"of the given observation space {observation_space}. \n"
+                )
+                message += f"{len(invalid_indices[0])} invalid indices: \n"
+
+                for index in zip(*invalid_indices):
+                    index_str = ",".join(map(str, index))
+                    message += (
+                        f"Expected: {lower_bounds[index]} <= obs[{index_str}] <= {upper_bounds[index]}, "
+                        f"actual value: {obs[index]} \n"
+                    )
+
+                raise AssertionError(message)
 
     assert observation_space.contains(obs), (
         f"The observation returned by the `{method_name}()` method "
diff --git a/stable_baselines3/version.txt b/stable_baselines3/version.txt
index a4a6a877e..736f6c84a 100644
--- a/stable_baselines3/version.txt
+++ b/stable_baselines3/version.txt
@@ -1 +1 @@
-2.1.0a3
+2.1.0a4
diff --git a/tests/test_env_checker.py b/tests/test_env_checker.py
index c0a5e0610..87cc177b7 100644
--- a/tests/test_env_checker.py
+++ b/tests/test_env_checker.py
@@ -42,15 +42,28 @@ def test_check_env_dict_action():
     [
         # Above upper bound
         (
-            spaces.Box(low=0.0, high=1.0, shape=(3,), dtype=np.float32),
+            spaces.Box(low=np.array([0.0, 0.0, 0.0]), high=np.array([2.0, 1.0, 1.0]), shape=(3,), dtype=np.float32),
             np.array([1.0, 1.5, 0.5], dtype=np.float32),
-            r"Expected: obs <= 1\.0, actual max value: 1\.5 at index 1",
+            r"Expected: 0\.0 <= obs\[1] <= 1\.0, actual value: 1\.5",
+        ),
+        # Above upper bound (multi-dim)
+        (
+            spaces.Box(low=-1.0, high=2.0, shape=(2, 3, 3, 1), dtype=np.float32),
+            3.0 * np.ones((2, 3, 3, 1), dtype=np.float32),
+            # Note: this is one of the 18 invalid indices
+            r"Expected: -1\.0 <= obs\[1,2,1,0\] <= 2\.0, actual value: 3\.0",
         ),
         # Below lower bound
         (
-            spaces.Box(low=0.0, high=2.0, shape=(3,), dtype=np.float32),
+            spaces.Box(low=np.array([0.0, -10.0, 0.0]), high=np.array([2.0, 1.0, 1.0]), shape=(3,), dtype=np.float32),
             np.array([-1.0, 1.5, 0.5], dtype=np.float32),
-            r"Expected: obs >= 0\.0, actual min value: -1\.0 at index 0",
+            r"Expected: 0\.0 <= obs\[0] <= 2\.0, actual value: -1\.0",
+        ),
+        # Below lower bound (multi-dim)
+        (
+            spaces.Box(low=-1.0, high=2.0, shape=(2, 3, 3, 1), dtype=np.float32),
+            -2 * np.ones((2, 3, 3, 1), dtype=np.float32),
+            r"18 invalid indices:",
         ),
         # Wrong dtype
         (
@@ -111,7 +124,7 @@ def step(self, action):
 
     test_env = TestEnv()
     with pytest.raises(AssertionError, match=error_message):
-        check_env(env=test_env)
+        check_env(env=test_env, warn=False)
 
 
 class LimitedStepsTestEnv(gym.Env):