diff --git a/coverage/files.py b/coverage/files.py
index 507496ffe..b5895cfca 100644
--- a/coverage/files.py
+++ b/coverage/files.py
@@ -24,8 +24,14 @@ def set_relative_directory():
     """Set the directory that `relative_filename` will be relative to."""
     global RELATIVE_DIR, CANONICAL_FILENAME_CACHE
 
+    # The current directory
+    abs_curdir = abs_file(os.curdir)
+    if not abs_curdir.endswith(os.sep):
+        # Suffix with separator only if not at the system root
+        abs_curdir = abs_curdir + os.sep
+
     # The absolute path to our current directory.
-    RELATIVE_DIR = os.path.normcase(abs_file(os.curdir) + os.sep)
+    RELATIVE_DIR = os.path.normcase(abs_curdir)
 
     # Cache of results of calling the canonical_filename() method, to
     # avoid duplicating work.
diff --git a/tests/test_files.py b/tests/test_files.py
index 5588c373d..28a98fb84 100644
--- a/tests/test_files.py
+++ b/tests/test_files.py
@@ -5,17 +5,14 @@
 
 import os
 import os.path
+from unittest import mock
 
 import pytest
 
-from coverage import env
-from coverage import files
+from coverage import env, files
 from coverage.exceptions import ConfigError
-from coverage.files import (
-    TreeMatcher, FnmatchMatcher, ModuleMatcher, PathAliases,
-    find_python_files, abs_file, actual_path, flat_rootname, fnmatches_to_regex,
-)
-
+from coverage.files import (FnmatchMatcher, ModuleMatcher, PathAliases, TreeMatcher, abs_file,
+                            actual_path, find_python_files, flat_rootname, fnmatches_to_regex)
 from tests.coveragetest import CoverageTest
 
 
@@ -67,6 +64,19 @@ def test_canonical_filename_ensure_cache_hit(self):
         assert 'sub/proj1/file1.py' in files.CANONICAL_FILENAME_CACHE
         assert files.canonical_filename('sub/proj1/file1.py') == self.abs_path('file1.py')
 
+    @pytest.mark.parametrize(
+        ["curdir", "sep"], [
+            ("/", "/"),
+            ("X:\\", "\\"),
+        ]
+    )
+    def test_relative_dir_for_root(self, curdir, sep):
+        with mock.patch.object(files.os, 'curdir', new=curdir):
+            with mock.patch.object(files.os, 'sep', new=sep):
+                with mock.patch('coverage.files.os.path.normcase', return_value=curdir):
+                    files.set_relative_directory()
+                    assert files.relative_directory() == curdir
+
 
 @pytest.mark.parametrize("original, flat", [
     ("abc.py", "abc_py"),