diff --git a/colorama/initialise.py b/colorama/initialise.py
index 6e01026..5074fd7 100644
--- a/colorama/initialise.py
+++ b/colorama/initialise.py
@@ -38,8 +38,10 @@ 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 orig_stdout is None:
+        orig_stdout = sys.stdout
+    if orig_stderr is None:
+        orig_stderr = sys.stderr
 
     if sys.stdout is None:
         wrapped_stdout = None
@@ -54,7 +56,7 @@ def init(autoreset=False, convert=None, strip=None, wrap=True):
 
     global atexit_done
     if not atexit_done:
-        atexit.register(reset_all)
+        atexit.register(deinit)
         atexit_done = True
 
 
diff --git a/tests/test_initialise.py b/tests/test_initialise.py
new file mode 100644
index 0000000..1a1e758
--- /dev/null
+++ b/tests/test_initialise.py
@@ -0,0 +1,31 @@
+import sys
+import unittest
+from unittest.mock import patch, MagicMock
+from colorama import init, deinit
+
+class TestColoramaInitialise(unittest.TestCase):
+
+    @patch('colorama.ansitowin32.AnsiToWin32')
+    def test_init_deinit(self, mock_ansitowin32):
+        original_stdout = sys.stdout
+        original_stderr = sys.stderr
+
+        # First call to init
+        init()
+        self.assertIsNotNone(sys.stdout)
+        self.assertIsNotNone(sys.stderr)
+
+        # Second call to init
+        init()
+        self.assertIsNotNone(sys.stdout)
+        self.assertIsNotNone(sys.stderr)
+
+        # Call deinit
+        deinit()
+
+        # Verify stdout and stderr are restored correctly
+        self.assertIs(sys.stdout, original_stdout)
+        self.assertIs(sys.stderr, original_stderr)
+
+if __name__ == '__main__':
+    unittest.main()
\ No newline at end of file