diff --git a/metric_learn/lmnn.py b/metric_learn/lmnn.py
index 8bdc4bf0..7c64418c 100644
--- a/metric_learn/lmnn.py
+++ b/metric_learn/lmnn.py
@@ -180,6 +180,10 @@ def fit(self, X, y):
     G, objective, total_active = self._loss_grad(X, L, dfG, k,
                                                  reg, target_neighbors,
                                                  label_inds)
+    if G is None:
+      # TODO: raise a warning
+      self.n_iter_ = 0
+      return self
 
     it = 1  # we already made one iteration
 
@@ -244,6 +248,8 @@ def _loss_grad(self, X, L, dfG, k, reg, target_neighbors, label_inds):
                                             Ni.argmax(axis=1)[:, None], 1)
     impostors = self._find_impostors(furthest_neighbors.ravel(), X,
                                      label_inds, L)
+    if not impostors:
+      return None, 0, 0
 
     g0 = _inplace_paired_L2(*Lx[impostors])