diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 023b360c5bb5c..78d73f3f93c4a 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -944,27 +944,29 @@ def select_n_frame(frame, columns, n, method, keep):
     -------
     nordered : DataFrame
     """
+    from pandas.core.series import Series
     if not is_list_like(columns):
         columns = [columns]
     else:
         columns = list(columns)
-    reverse = method == 'nlargest'
+
+    ascending = method == 'nsmallest'
+    tmp = Series(frame.index)
+    frame.reset_index(inplace=True, drop=True)
+    cur_frame = frame
+
     for i, column in enumerate(columns):
-        series = frame[column]
-        if reverse:
-            inds = series.argsort()[::-1][:n]
-        else:
-            inds = series.argsort()[:n]
-        values = series.iloc[inds]
-        if i != len(columns) - 1 and values.duplicated().any():
-            # This series has duplicate values => we must consider all rows in
-            # frame that match `values`
-            # The first condition is for the last column. In this case we don't
-            # care if there are duplicates => no need to do the check
-            frame = frame[series.isin(values)]
+        series = cur_frame[column]
+        values = getattr(series, method)(n, keep=keep)
+        if i + 1 == len(columns) or values.is_unique:
+            cur_frame = cur_frame.reindex(values.index)
         else:
-            break
-    return frame.take(inds)
+            cur_frame = cur_frame[series.isin(values)].sort_values(
+                column, ascending=ascending
+            )
+    frame.index = tmp.ix[frame.index]
+    cur_frame.index = tmp.ix[cur_frame.index]
+    return cur_frame
 
 
 def _finalize_nsmallest(arr, kth_val, n, keep, narr):