diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index 1024ab6..ddcd2cc 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -2767,10 +2767,19 @@
     if sys.platform.startswith(('linux', 'freebsd')):
         try:
             names = os.listdir("/proc/self/fd")
-            return len(names)
+            # Substract one because listdir() opens internally a file
+            # descriptor to list the content of the /proc/self/fd/ directory.
+            return len(names) - 1
         except FileNotFoundError:
             pass
 
+    MAXFD = 256
+    if hasattr(os, 'sysconf'):
+        try:
+            MAXFD = os.sysconf("SC_OPEN_MAX")
+        except OSError:
+            pass
+
     old_modes = None
     if sys.platform == 'win32':
         # bpo-25306, bpo-31009: Call CrtSetReportMode() to not kill the process
@@ -2788,13 +2797,6 @@
                                 msvcrt.CRT_ASSERT):
                 old_modes[report_type] = msvcrt.CrtSetReportMode(report_type, 0)
 
-    MAXFD = 256
-    if hasattr(os, 'sysconf'):
-        try:
-            MAXFD = os.sysconf("SC_OPEN_MAX")
-        except OSError:
-            pass
-
     try:
         count = 0
         for fd in range(MAXFD):
diff --git a/Lib/test/test_support.py b/Lib/test/test_support.py
index 36d5f84..89f1fbf 100644
--- a/Lib/test/test_support.py
+++ b/Lib/test/test_support.py
@@ -569,6 +569,17 @@
             self.assertTrue(support.match_test(test_access))
             self.assertFalse(support.match_test(test_chdir))
 
+    def test_fd_count(self):
+        # We cannot test the absolute value of fd_count(): on old Linux
+        # kernel or glibc versions, os.urandom() keeps a FD open on
+        # /dev/urandom device and Python has 4 FD opens instead of 3.
+        start = support.fd_count()
+        fd = os.open(__file__, os.O_RDONLY)
+        try:
+            more = support.fd_count()
+        finally:
+            os.close(fd)
+        self.assertEqual(more - start, 1)
 
     # XXX -follows a list of untested API
     # make_legacy_pyc