diff --git a/fancyimpute/solver.py b/fancyimpute/solver.py
index 2f966a7..54e8e66 100644
--- a/fancyimpute/solver.py
+++ b/fancyimpute/solver.py
@@ -182,17 +182,21 @@ def fit_transform(self, X, y=None):
                 "Expected %s.fill() to return NumPy array but got %s" % (
                     self.__class__.__name__,
                     type(X_filled)))
-
-        X_result = self.solve(X_filled, missing_mask)
-        if not isinstance(X_result, np.ndarray):
-            raise TypeError(
-                "Expected %s.solve() to return NumPy array but got %s" % (
-                    self.__class__.__name__,
-                    type(X_result)))
-
-        X_result = self.project_result(X=X_result)
-        X_result[observed_mask] = X_original[observed_mask]
-        return X_result
+        # check if there is any missing data
+        if ((missing_mask == True).any()):
+            X_result = self.solve(X_filled, missing_mask)
+
+            if not isinstance(X_result, np.ndarray):
+                raise TypeError(
+                    "Expected %s.solve() to return NumPy array but got %s" % (
+                        self.__class__.__name__,
+                        type(X_result)))
+
+            X_result = self.project_result(X=X_result)
+            X_result[observed_mask] = X_original[observed_mask]
+            return X_result
+        else:
+            return X_filled
 
     def fit(self, X, y=None):
         """
diff --git a/test/test_soft_impute.py b/test/test_soft_impute.py
index 9d14bbf..adb5fd8 100644
--- a/test/test_soft_impute.py
+++ b/test/test_soft_impute.py
@@ -1,8 +1,9 @@
 from low_rank_data import XY, XY_incomplete, missing_mask
 from common import reconstruction_error
-
+import numpy as np
 from fancyimpute import SoftImpute
 
+
 def test_soft_impute_with_low_rank_random_matrix():
     solver = SoftImpute()
     XY_completed = solver.fit_transform(XY_incomplete)
@@ -13,5 +14,14 @@ def test_soft_impute_with_low_rank_random_matrix():
         name="SoftImpute")
     assert missing_mae < 0.1, "Error too high!"
 
+
+# test if the solver for a submodel is running for a numpy array without any missing data
+def check_for_no_missing_data():
+    X = np.ones((5, 5))
+    Xf = SoftImpute().fit_transform(X)
+    assert (Xf.all() == X.all())
+
+
 if __name__ == "__main__":
     test_soft_impute_with_low_rank_random_matrix()
+    check_for_no_missing_data()