diff --git a/tslearn/metrics/ctw.py b/tslearn/metrics/ctw.py
index f3d48cef..97546b73 100644
--- a/tslearn/metrics/ctw.py
+++ b/tslearn/metrics/ctw.py
@@ -1,3 +1,8 @@
+"""
+The :mod:`tslearn.metrics:ctc` module provides utilities related to
+Canonical Time Warping.
+"""
+
 import numpy as np
 from sklearn.cross_decomposition import CCA
 
@@ -157,7 +162,7 @@ def ctw_path(
     # (possibly truncated to a fixed number of features) inputs
     seq1_tr = s1 @ be.eye(s1.shape[1], n_components, dtype=be.float64)
     seq2_tr = s2 @ be.eye(s2.shape[1], n_components, dtype=be.float64)
-    current_path, score_match = dtw_path(
+    current_path, current_score = dtw_path(
         seq1_tr,
         seq2_tr,
         global_constraint=global_constraint,
@@ -165,7 +170,6 @@ def ctw_path(
         itakura_max_slope=itakura_max_slope,
         be=be,
     )
-    current_score = score_match
 
     if verbose:
         print("Iteration 0, score={}".format(current_score))
@@ -176,7 +180,7 @@ def ctw_path(
         cca.fit(Wx @ s1, Wy @ s2)
         seq1_tr, seq2_tr = cca.transform(s1, s2)
 
-        current_path, score_match = dtw_path(
+        new_path, new_score = dtw_path(
             seq1_tr,
             seq2_tr,
             global_constraint=global_constraint,
@@ -185,10 +189,10 @@ def ctw_path(
             be=be,
         )
 
-        if np.array_equal(current_path, current_path):
+        if np.array_equal(current_path, new_path):
             break
 
-        current_score = score_match
+        current_path, current_score = new_path, new_score
 
         if verbose:
             print("Iteration {}, score={}".format(it + 1, current_score))
@@ -329,7 +333,7 @@ def cdist_ctw(
         If shape is (n_ts1, sz1), the dataset is composed of univariate time series.
         If shape is (sz1,), the dataset is composed of a unique univariate time series.
     dataset2 : None or array-like, shape=(n_ts2, sz2, d) or (n_ts2, sz2) or (sz2,) (default: None)
-        Another dataset of time series. 
+        Another dataset of time series.
         If `None`, self-similarity of `dataset1` is returned.
         If shape is (n_ts2, sz2), the dataset is composed of univariate time series.
         If shape is (sz2,), the dataset is composed of a unique univariate time series.
diff --git a/tslearn/tests/test_metrics.py b/tslearn/tests/test_metrics.py
index 20d93c41..49fe2704 100644
--- a/tslearn/tests/test_metrics.py
+++ b/tslearn/tests/test_metrics.py
@@ -77,6 +77,22 @@ def test_ctw():
             np.testing.assert_allclose(dist, 1.0)
             assert backend.belongs_to_backend(dist)
 
+            x = [[1, 1],  [3, 4], [126, 126]]
+            y = [[1, 1.], [3., 3], [4., 4], [2., 2], [0, 0], [127, 127]]
+            dist_0 = tslearn.metrics.ctw_path(
+                cast(x, array_type),
+                cast(y, array_type),
+                max_iter=2,
+                be=be
+            )[2]
+            dist_1 = tslearn.metrics.ctw_path(
+                cast(x, array_type),
+                cast(y, array_type),
+                max_iter=3,
+                be=be
+            )[2]
+            assert dist_0 >= dist_1
+
             # dtw
             n1, n2, d1, d2 = 15, 10, 3, 1
             rng = np.random.RandomState(0)