diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -610,6 +610,19 @@ class IOTest(unittest.TestCase):
         self.assertEqual(rawio.read(2), None)
         self.assertEqual(rawio.read(2), b"")
 
+    def test_fileio_closefd(self):
+        # Issue #4841
+        with self.open(__file__, 'rb') as f1, \
+             self.open(__file__, 'rb') as f2:
+            fileio = self.FileIO(f1.fileno(), closefd=False)
+            # .__init__() must not close f1
+            fileio.__init__(f2.fileno(), closefd=False)
+            f1.readline()
+            # .close() must not close f2
+            fileio.close()
+            f2.readline()
+
+
 class CIOTest(IOTest):
     pass
 
diff --git a/Modules/_io/fileio.c b/Modules/_io/fileio.c
--- a/Modules/_io/fileio.c
+++ b/Modules/_io/fileio.c
@@ -233,9 +233,13 @@ fileio_init(PyObject *oself, PyObject *a
 
     assert(PyFileIO_Check(oself));
     if (self->fd >= 0) {
-        /* Have to close the existing file first. */
-        if (internal_close(self) < 0)
-            return -1;
+        if (self->closefd) {
+            /* Have to close the existing file first. */
+            if (internal_close(self) < 0)
+                return -1;
+        }
+        else
+            self->fd = -1;
     }
 
     if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|si:fileio",