diff --git a/maint_tools/test_docstrings.py b/maint_tools/test_docstrings.py
index 50678eb78a204..f6b5b2f8f515c 100644
--- a/maint_tools/test_docstrings.py
+++ b/maint_tools/test_docstrings.py
@@ -30,7 +30,6 @@
     "sklearn.cluster._optics.compute_optics_graph",
     "sklearn.cluster._spectral.spectral_clustering",
     "sklearn.compose._column_transformer.make_column_transformer",
-    "sklearn.covariance._empirical_covariance.empirical_covariance",
     "sklearn.covariance._graph_lasso.graphical_lasso",
     "sklearn.covariance._robust_covariance.fast_mcd",
     "sklearn.covariance._shrunk_covariance.ledoit_wolf",
diff --git a/sklearn/covariance/_empirical_covariance.py b/sklearn/covariance/_empirical_covariance.py
index bea05ac0279e5..631423da242f6 100644
--- a/sklearn/covariance/_empirical_covariance.py
+++ b/sklearn/covariance/_empirical_covariance.py
@@ -49,19 +49,18 @@ def log_likelihood(emp_cov, precision):
 
 
 def empirical_covariance(X, *, assume_centered=False):
-    """Computes the Maximum likelihood covariance estimator
-
+    """Compute the Maximum likelihood covariance estimator.
 
     Parameters
     ----------
     X : ndarray of shape (n_samples, n_features)
-        Data from which to compute the covariance estimate
+        Data from which to compute the covariance estimate.
 
     assume_centered : bool, default=False
-        If True, data will not be centered before computation.
+        If `True`, data will not be centered before computation.
         Useful when working with data whose mean is almost, but not exactly
         zero.
-        If False, data will be centered before computation.
+        If `False`, data will be centered before computation.
 
     Returns
     -------