diff --git a/colorama/initialise.py b/colorama/initialise.py
index 430d066..62ee510 100644
--- a/colorama/initialise.py
+++ b/colorama/initialise.py
@@ -28,19 +28,23 @@ def init(autoreset=False, convert=None, strip=None, wrap=True):
     global wrapped_stdout, wrapped_stderr
     global orig_stdout, orig_stderr
 
-    orig_stdout = sys.stdout
-    orig_stderr = sys.stderr
-
-    if sys.stdout is None:
-        wrapped_stdout = None
-    else:
-        sys.stdout = wrapped_stdout = \
-            wrap_stream(orig_stdout, convert, strip, autoreset, wrap)
-    if sys.stderr is None:
-        wrapped_stderr = None
-    else:
-        sys.stderr = wrapped_stderr = \
-            wrap_stream(orig_stderr, convert, strip, autoreset, wrap)
+    if orig_stdout is None:
+        orig_stdout = sys.stdout
+
+        if sys.stdout is None:
+            wrapped_stdout = None
+        else:
+            sys.stdout = wrapped_stdout = \
+                wrap_stream(orig_stdout, convert, strip, autoreset, wrap)
+
+    if orig_stderr is None:
+        orig_stderr = sys.stderr
+
+        if sys.stderr is None:
+            wrapped_stderr = None
+        else:
+            sys.stderr = wrapped_stderr = \
+                wrap_stream(orig_stderr, convert, strip, autoreset, wrap)
 
     global atexit_done
     if not atexit_done: