diff --git a/pandas/core/internals.py b/pandas/core/internals.py
index fd998e5060b5f..f171915eeaccc 100644
--- a/pandas/core/internals.py
+++ b/pandas/core/internals.py
@@ -666,14 +666,24 @@ def convert(self, convert_dates = True, convert_numeric = True, copy = True):
 
         # attempt to create new type blocks
         blocks = []
-        for i, c in enumerate(self.items):
-            values = self.get(c)
-
-            values = com._possibly_convert_objects(values, convert_dates=convert_dates, convert_numeric=convert_numeric)
-            values = _block_shape(values)
-            items = self.items.take([i])
-            newb = make_block(values, items, self.ref_items)
-            blocks.append(newb)
+        if self.items.is_unique:
+            for i,c in enumerate(self.items):
+                values = self.get(c)
+
+                values = com._possibly_convert_objects(values, convert_dates=convert_dates, convert_numeric=convert_numeric)
+                values = _block_shape(values)
+                items = self.items.take([i])
+                newb = make_block(values, items, self.ref_items)
+                blocks.append(newb)
+        else:
+            for i in  range(len(self.items)):
+                values = self.values[i]
+
+                values = com._possibly_convert_objects(values, convert_dates=convert_dates, convert_numeric=convert_numeric)
+                values = _block_shape(values)
+                items = self.items.take([i])
+                newb = make_block(values, items, self.ref_items)
+                blocks.append(newb)
 
         return blocks
 
diff --git a/pandas/tests/test_frame.py b/pandas/tests/test_frame.py
index 626592958147e..c3b2c39c803fe 100644
--- a/pandas/tests/test_frame.py
+++ b/pandas/tests/test_frame.py
@@ -7171,6 +7171,16 @@ def test_applymap(self):
         result = df.applymap(lambda x: x)
         self.assert_(result.dtypes[0] == object)
 
+        # GH2786
+
+        df = DataFrame(np.random.random((3,4)))
+        df.columns = Index(['a','a','a','a'])
+        res = df.applymap(str)
+        assert_series_equal(res.icol(0),Series(map(str,df.icol(0).values)))
+        assert_series_equal(res.icol(1),Series(map(str,df.icol(1).values)))
+        assert_series_equal(res.icol(2),Series(map(str,df.icol(2).values)))
+        assert_series_equal(res.icol(3),Series(map(str,df.icol(3).values)))
+
     def test_filter(self):
         # items