diff --git a/Lib/fileinput.py b/Lib/fileinput.py
@@ -330,7 +330,7 @@ def _readline(self):
        else:
            if self._inplace:
                self._backupfilename = (
-                    self._filename + (self._backup or ".bak"))
                try:
                    os.unlink(self._backupfilename)
                except OSError:

diff --git a/Lib/test/test_fileinput.py b/Lib/test/test_fileinput.py
@@ -544,6 +544,19 @@ def test_pathlib_file(self):
        finally:
            remove_tempfiles(t1)


class MockFileInput:
    """A class that mocks out fileinput.FileInput for use during unit tests"""

diff --git a/Misc/NEWS.d/next/Library/2017-08-29-07-14-14.bpo-31281.DcFyNs.rst b/Misc/NEWS.d/next/Library/2017-08-29-07-14-14.bpo-31281.DcFyNs.rst
@@ -0,0 +1,2 @@