diff --git a/HISTORY.md b/HISTORY.md
index 2ec365f..6d9e0ce 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -1,3 +1,8 @@
+unreleased
+==========
+
+  * Fix encoding unpaired surrogates at start/end of string
+
 1.0.0 / 2016-06-08
 ==================
 
diff --git a/index.js b/index.js
index 6ac7738..ae77cc9 100644
--- a/index.js
+++ b/index.js
@@ -26,7 +26,7 @@ var ENCODE_CHARS_REGEXP = /(?:[^\x21\x25\x26-\x3B\x3D\x3F-\x5B\x5D\x5F\x61-\x7A\
  * @private
  */
 
-var UNMATCHED_SURROGATE_PAIR_REGEXP = /([^\uD800-\uDBFF])[\uDC00-\uDFFF]|[\uD800-\uDBFF]([^\uDC00-\uDFFF])/g
+var UNMATCHED_SURROGATE_PAIR_REGEXP = /(^|[^\uD800-\uDBFF])[\uDC00-\uDFFF]|[\uD800-\uDBFF]([^\uDC00-\uDFFF]|$)/g
 
 /**
  * String to replace unmatched surrogate pair with.
diff --git a/test/test.js b/test/test.js
index d5c543a..5b215ec 100644
--- a/test/test.js
+++ b/test/test.js
@@ -76,8 +76,18 @@ describe('encodeUrl(url)', function () {
       assert.equal(encodeUrl('http://localhost/\uD83D\uDC7B snow.html'), 'http://localhost/%F0%9F%91%BB%20snow.html')
     })
 
-    it('should encode unpaired surrogate pairs as replacement character', function () {
-      assert.equal(encodeUrl('http://localhost/\uD83Dfoo\uDC7B <\uDC7B\uD83D>.html'), 'http://localhost/%EF%BF%BDfoo%EF%BF%BD%20%3C%EF%BF%BD%EF%BF%BD%3E.html')
+    describe('when unpaired', function () {
+      it('should encode as replacement character', function () {
+        assert.equal(encodeUrl('http://localhost/\uD83Dfoo\uDC7B <\uDC7B\uD83D>.html'), 'http://localhost/%EF%BF%BDfoo%EF%BF%BD%20%3C%EF%BF%BD%EF%BF%BD%3E.html')
+      })
+
+      it('should encode at end of string', function () {
+        assert.equal(encodeUrl('http://localhost/\uD83D'), 'http://localhost/%EF%BF%BD')
+      })
+
+      it('should encode at start of string', function () {
+        assert.equal(encodeUrl('\uDC7Bfoo'), '%EF%BF%BDfoo')
+      })
     })
   })
 })