diff --git a/Lib/encodings/utf_16.py b/Lib/encodings/utf_16.py
index 5500c06..809bc9a 100644
--- a/Lib/encodings/utf_16.py
+++ b/Lib/encodings/utf_16.py
@@ -103,17 +103,23 @@
 
 class StreamWriter(codecs.StreamWriter):
     def __init__(self, stream, errors='strict'):
-        self.bom_written = False
         codecs.StreamWriter.__init__(self, stream, errors)
+        self.encoder = None
+
+    def reset(self):
+        codecs.StreamWriter.reset(self)
+        self.encoder = None
 
     def encode(self, input, errors='strict'):
-        self.bom_written = True
-        result = codecs.utf_16_encode(input, errors)
-        if sys.byteorder == 'little':
-            self.encode = codecs.utf_16_le_encode
+        if self.encoder is None:
+            result = codecs.utf_16_encode(input, errors)
+            if sys.byteorder == 'little':
+                self.encoder = codecs.utf_16_le_encode
+            else:
+                self.encoder = codecs.utf_16_be_encode
+            return result
         else:
-            self.encode = codecs.utf_16_be_encode
-        return result
+            return self.encoder(input, errors)
 
 class StreamReader(codecs.StreamReader):
 
diff --git a/Lib/encodings/utf_32.py b/Lib/encodings/utf_32.py
index f0b7709..c052928 100644
--- a/Lib/encodings/utf_32.py
+++ b/Lib/encodings/utf_32.py
@@ -98,17 +98,23 @@
 
 class StreamWriter(codecs.StreamWriter):
     def __init__(self, stream, errors='strict'):
-        self.bom_written = False
+        self.encoder = None
         codecs.StreamWriter.__init__(self, stream, errors)
 
+    def reset(self):
+        codecs.StreamWriter.reset(self)
+        self.encoder = None
+
     def encode(self, input, errors='strict'):
-        self.bom_written = True
-        result = codecs.utf_32_encode(input, errors)
-        if sys.byteorder == 'little':
-            self.encode = codecs.utf_32_le_encode
+        if self.encoder is None:
+            result = codecs.utf_32_encode(input, errors)
+            if sys.byteorder == 'little':
+                self.encoder = codecs.utf_32_le_encode
+            else:
+                self.encoder = codecs.utf_32_be_encode
+            return result
         else:
-            self.encode = codecs.utf_32_be_encode
-        return result
+            return self.encoder(input, errors)
 
 class StreamReader(codecs.StreamReader):