diff --git a/src/fonts.js b/src/fonts.js
index 10c0819f7..bdd04d3a7 100644
--- a/src/fonts.js
+++ b/src/fonts.js
@@ -3903,9 +3903,10 @@ var Font = (function FontClosure() {
 
         var usedUnicodes = [];
         var unassignedUnicodeItems = [];
+        var toFontChar = this.cidToFontChar || this.toFontChar;
         for (var i = 1; i < numGlyphs; i++) {
           var cid = gidToCidMap[i] || i;
-          var unicode = this.toFontChar[cid];
+          var unicode = toFontChar[cid];
           if (!unicode || typeof unicode !== 'number' ||
               isSpecialUnicode(unicode) || unicode in usedUnicodes) {
             unassignedUnicodeItems.push(i);
@@ -3915,21 +3916,25 @@ var Font = (function FontClosure() {
           glyphs.push({ unicode: unicode, code: cid });
           ids.push(i);
         }
-        // trying to fit as many unassigned symbols as we can
-        // in the range allocated for the user defined symbols
-        var unusedUnicode = CMAP_GLYPH_OFFSET;
-        for (var j = 0, jj = unassignedUnicodeItems.length; j < jj; j++) {
-          var i = unassignedUnicodeItems[j];
-          var cid = gidToCidMap[i] || i;
-          while (unusedUnicode in usedUnicodes)
-            unusedUnicode++;
-          if (unusedUnicode >= CMAP_GLYPH_OFFSET + GLYPH_AREA_SIZE)
-            break;
-          var unicode = unusedUnicode++;
-          this.toFontChar[cid] = unicode;
-          usedUnicodes[unicode] = true;
-          glyphs.push({ unicode: unicode, code: cid });
-          ids.push(i);
+        // unassigned codepoints will never be used for non-Identity CMap
+        // because the input will be Unicode
+        if (!this.cidToFontChar) {
+          // trying to fit as many unassigned symbols as we can
+          // in the range allocated for the user defined symbols
+          var unusedUnicode = CMAP_GLYPH_OFFSET;
+          for (var j = 0, jj = unassignedUnicodeItems.length; j < jj; j++) {
+            var i = unassignedUnicodeItems[j];
+            var cid = gidToCidMap[i] || i;
+            while (unusedUnicode in usedUnicodes)
+              unusedUnicode++;
+            if (unusedUnicode >= CMAP_GLYPH_OFFSET + GLYPH_AREA_SIZE)
+              break;
+            var unicode = unusedUnicode++;
+            this.toFontChar[cid] = unicode;
+            usedUnicodes[unicode] = true;
+            glyphs.push({ unicode: unicode, code: cid });
+            ids.push(i);
+          }
         }
       } else {
         this.useToFontChar = true;
@@ -4394,6 +4399,11 @@ var Font = (function FontClosure() {
       if (cidEncoding.indexOf('Identity-') !== 0) {
         // input is already Unicode for non-Identity CMap encodings.
         this.cidToUnicode = [];
+        // For CIDFontType2, however, we need cid-to-Unicode conversion
+        // to rebuild cmap.
+        if (properties.type == 'CIDFontType2') {
+          this.cidToFontChar = cidToUnicodeMap;
+        }
       } else {
         // We don't have to do reverse conversions if the string is
         // already CID.
@@ -4494,6 +4504,8 @@ var Font = (function FontClosure() {
             var cid = this.unicodeToCID[charcode] || charcode;
             width = this.widths[cid];
             vmetric = this.vmetrics && this.vmetrics[cid];
+            fontCharCode = charcode;
+            break;
           }
           fontCharCode = this.toFontChar[charcode] || charcode;
           break;
diff --git a/test/pdfs/ohkubo-SS04.pdf.link b/test/pdfs/ohkubo-SS04.pdf.link
new file mode 100644
index 000000000..979ad7bc7
--- /dev/null
+++ b/test/pdfs/ohkubo-SS04.pdf.link
@@ -0,0 +1 @@
+http://www.sapid.org/html2/PDF-ja/ohkubo-SS04.pdf
\ No newline at end of file
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 4cce61f7f..9b1c4ac58 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -930,6 +930,13 @@
       "rounds": 1,
       "type": "eq"
     },
+    {  "id": "ohkubo-ss04",
+      "file": "pdfs/ohkubo-SS04.pdf",
+      "md5": "b8c334073ff5be74fac1f36130943ea5",
+      "rounds": 1,
+      "link": true,
+      "type": "eq"
+    },
     {  "id": "sfaa_japanese",
       "file": "pdfs/SFAA_Japanese.pdf",
       "md5": "b961bbc0d05bdd6d91041bca60ec8e8b",