diff --git a/sklearn/_loss/tests/test_link.py b/sklearn/_loss/tests/test_link.py
index 435361eaa50f1..c083883d3d650 100644
--- a/sklearn/_loss/tests/test_link.py
+++ b/sklearn/_loss/tests/test_link.py
@@ -58,20 +58,21 @@ def test_is_in_range(interval):
 
 
 @pytest.mark.parametrize("link", LINK_FUNCTIONS)
-def test_link_inverse_identity(link):
+def test_link_inverse_identity(link, global_random_seed):
     # Test that link of inverse gives identity.
-    rng = np.random.RandomState(42)
+    rng = np.random.RandomState(global_random_seed)
     link = link()
     n_samples, n_classes = 100, None
+    # The values for `raw_prediction` are limited from -20 to 20 because in the
+    # class `LogitLink` the term `expit(x)` comes very close to 1 for large
+    # positive x and therefore loses precision.
     if link.is_multiclass:
         n_classes = 10
-        raw_prediction = rng.normal(loc=0, scale=10, size=(n_samples, n_classes))
+        raw_prediction = rng.uniform(low=-20, high=20, size=(n_samples, n_classes))
         if isinstance(link, MultinomialLogit):
             raw_prediction = link.symmetrize_raw_prediction(raw_prediction)
     else:
-        # So far, the valid interval of raw_prediction is (-inf, inf) and
-        # we do not need to distinguish.
-        raw_prediction = rng.normal(loc=0, scale=10, size=(n_samples))
+        raw_prediction = rng.uniform(low=-20, high=20, size=(n_samples))
 
     assert_allclose(link.link(link.inverse(raw_prediction)), raw_prediction)
     y_pred = link.inverse(raw_prediction)