diff --git a/src/core/fonts.js b/src/core/fonts.js
index add8fd973..39a74e2d0 100644
--- a/src/core/fonts.js
+++ b/src/core/fonts.js
@@ -3635,6 +3635,22 @@ var Type1Font = (function Type1FontClosure() {
 
     getGlyphMapping: function Type1Font_getGlyphMapping(properties) {
       var charstrings = this.charstrings;
+
+      if (properties.composite) {
+        const charCodeToGlyphId = Object.create(null);
+        // Map CIDs directly to GIDs.
+        for (
+          let glyphId = 0, charstringsLen = charstrings.length;
+          glyphId < charstringsLen;
+          glyphId++
+        ) {
+          const charCode = properties.cMap.charCodeOf(glyphId);
+          // Add 1 because glyph 0 is duplicated.
+          charCodeToGlyphId[charCode] = glyphId + 1;
+        }
+        return charCodeToGlyphId;
+      }
+
       var glyphNames = [".notdef"],
         glyphId;
       for (glyphId = 0; glyphId < charstrings.length; glyphId++) {
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index 648de4c34..a6ef9da6a 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -206,6 +206,7 @@
 !bug1011159.pdf
 !issue5734.pdf
 !issue4875.pdf
+!issue11740_reduced.pdf
 !issue4881.pdf
 !issue5994.pdf
 !issue6151.pdf
diff --git a/test/pdfs/issue11740_reduced.pdf b/test/pdfs/issue11740_reduced.pdf
new file mode 100644
index 000000000..069bf0514
Binary files /dev/null and b/test/pdfs/issue11740_reduced.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 9429ca6f9..73f94005e 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -904,6 +904,12 @@
        "link": false,
        "type": "eq"
     },
+    {  "id": "issue11740",
+       "file": "pdfs/issue11740_reduced.pdf",
+       "md5": "f3f2957f171af52229c6e749e8a5572b",
+       "rounds": 1,
+       "type": "eq"
+    },
     {  "id": "issue10491",
        "file": "pdfs/issue10491.pdf",
        "md5": "0759ec46739b13bb0b66170a18d33d4f",