diff --git a/src/lib.rs b/src/lib.rs
index a128436..dd1fd65 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1337,7 +1337,7 @@ impl<'a> Face<'a> {
 
             bdat,
             cbdt,
-            cff: raw_tables.cff.and_then(cff::Table::parse),
+            cff: raw_tables.cff.and_then(|data| cff::Table::parse(data, head.units_per_em)),
             cmap: raw_tables.cmap.and_then(cmap::Table::parse),
             colr,
             ebdt,
diff --git a/src/tables/cff/cff1.rs b/src/tables/cff/cff1.rs
index 428884b..6747a73 100644
--- a/src/tables/cff/cff1.rs
+++ b/src/tables/cff/cff1.rs
@@ -122,7 +122,7 @@ pub(crate) struct CIDMetadata<'a> {
 
 /// An affine transformation matrix.
 #[allow(missing_docs)]
-#[derive(Clone, Copy, Debug)]
+#[derive(Clone, Copy, Debug, PartialEq)]
 pub struct Matrix {
     pub sx: f32,
     pub ky: f32,
@@ -374,9 +374,12 @@ fn parse_char_string(
         local_subrs,
     };
 
+    let transform = (metadata.units_per_em, metadata.matrix());
+    let transform = (transform != (1000, Matrix::default())).then_some(transform);
     let mut inner_builder = Builder {
         builder,
         bbox: RectF::new(),
+        transform,
     };
 
     let stack = ArgumentsStack {
@@ -846,11 +849,15 @@ pub struct Table<'a> {
     matrix: Matrix,
     char_strings: Index<'a>,
     kind: FontKind<'a>,
+
+    // Copy of Face::units_per_em().
+    // Required to do glyph outlining, since coordinates must be scaled up by this before applying the `matrix`.
+    units_per_em: u16,
 }
 
 impl<'a> Table<'a> {
     /// Parses a table from raw data.
-    pub fn parse(data: &'a [u8]) -> Option<Self> {
+    pub fn parse(data: &'a [u8], units_per_em: u16) -> Option<Self> {
         let mut s = Stream::new(data);
 
         // Parse Header.
@@ -930,6 +937,7 @@ impl<'a> Table<'a> {
             matrix,
             char_strings,
             kind,
+            units_per_em,
         })
     }
 
diff --git a/src/tables/cff/cff2.rs b/src/tables/cff/cff2.rs
index acb9b90..68e7a20 100644
--- a/src/tables/cff/cff2.rs
+++ b/src/tables/cff/cff2.rs
@@ -250,6 +250,7 @@ fn parse_char_string(
     let mut inner_builder = Builder {
         builder,
         bbox: RectF::new(),
+        transform: None,
     };
 
     let stack = ArgumentsStack {
diff --git a/src/tables/cff/mod.rs b/src/tables/cff/mod.rs
index a88738c..9b6c14d 100644
--- a/src/tables/cff/mod.rs
+++ b/src/tables/cff/mod.rs
@@ -45,23 +45,29 @@ pub enum CFFError {
 pub(crate) struct Builder<'a> {
     builder: &'a mut dyn OutlineBuilder,
     bbox: RectF,
+    transform: Option<(u16, cff1::Matrix)>,
 }
 
 impl<'a> Builder<'a> {
     #[inline]
     fn move_to(&mut self, x: f32, y: f32) {
+        let (x, y) = self.transform(x, y);
         self.bbox.extend_by(x, y);
         self.builder.move_to(x, y);
     }
 
     #[inline]
     fn line_to(&mut self, x: f32, y: f32) {
+        let (x, y) = self.transform(x, y);
         self.bbox.extend_by(x, y);
         self.builder.line_to(x, y);
     }
 
     #[inline]
     fn curve_to(&mut self, x1: f32, y1: f32, x2: f32, y2: f32, x: f32, y: f32) {
+        let (x1, y1) = self.transform(x1, y1);
+        let (x2, y2) = self.transform(x2, y2);
+        let (x, y) = self.transform(x, y);
         self.bbox.extend_by(x1, y1);
         self.bbox.extend_by(x2, y2);
         self.bbox.extend_by(x, y);
@@ -72,6 +78,21 @@ impl<'a> Builder<'a> {
     fn close(&mut self) {
         self.builder.close();
     }
+
+    #[inline]
+    fn transform(&self, x: f32, y: f32) -> (f32, f32) {
+        let (units_per_em, matrix) = if let Some(transform) = self.transform {
+            transform
+        } else {
+            return (x, y);
+        };
+        let (mut tx, mut ty) = (x, y);
+        tx = tx * matrix.sx + ty * matrix.kx + matrix.tx;
+        ty = tx * matrix.ky + ty * matrix.sy + matrix.ty;
+        tx *= units_per_em as f32;
+        ty *= units_per_em as f32;
+        (tx, ty)
+    }
 }
 
 /// A type-safe wrapper for string ID.
diff --git a/tests/tables/cff1.rs b/tests/tables/cff1.rs
index 261e1d5..dd59751 100644
--- a/tests/tables/cff1.rs
+++ b/tests/tables/cff1.rs
@@ -312,7 +312,7 @@ fn unsupported_version() {
         UInt8(0), // absolute offset
     ]);
 
-    assert!(cff::Table::parse(&data).is_none());
+    assert!(cff::Table::parse(&data, 1000).is_none());
 }
 
 #[test]
@@ -360,7 +360,7 @@ fn non_default_header_size() {
         UInt8(operator::ENDCHAR),
     ]);
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let rect = table.outline(GlyphId(0), &mut builder).unwrap();
 
@@ -377,7 +377,7 @@ macro_rules! test_cs_with_subrs {
         #[test]
         fn $name() {
             let data = gen_cff($glob, $loc, $values);
-            let table = cff::Table::parse(&data).unwrap();
+            let table = cff::Table::parse(&data, 1000).unwrap();
             let mut builder = Builder(String::new());
             let rect = table.outline(GlyphId(0), &mut builder).unwrap();
 
@@ -398,7 +398,7 @@ macro_rules! test_cs_err {
         #[test]
         fn $name() {
             let data = gen_cff(&[], &[], $values);
-            let table = cff::Table::parse(&data).unwrap();
+            let table = cff::Table::parse(&data, 1000).unwrap();
             let mut builder = Builder(String::new());
             let res = table.outline(GlyphId(0), &mut builder);
             assert_eq!(res.unwrap_err(), $err);
@@ -575,7 +575,7 @@ test_cs!(vv_curve_to_with_x, &[
 #[test]
 fn only_endchar() {
     let data = gen_cff(&[], &[], &[UInt8(operator::ENDCHAR)]);
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     assert!(table.outline(GlyphId(0), &mut builder).is_err());
 }
@@ -800,7 +800,7 @@ fn endchar_in_subr_with_extra_data_1() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::DataAfterEndChar);
@@ -827,7 +827,7 @@ fn endchar_in_subr_with_extra_data_2() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::DataAfterEndChar);
@@ -854,7 +854,7 @@ fn subr_without_return() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::DataAfterEndChar);
@@ -876,7 +876,7 @@ fn recursive_local_subr() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::NestingLimitReached);
@@ -898,7 +898,7 @@ fn recursive_global_subr() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::NestingLimitReached);
@@ -923,7 +923,7 @@ fn recursive_mixed_subr() {
         ]
     );
 
-    let table = cff::Table::parse(&data).unwrap();
+    let table = cff::Table::parse(&data, 1000).unwrap();
     let mut builder = Builder(String::new());
     let res = table.outline(GlyphId(0), &mut builder);
     assert_eq!(res.unwrap_err(), CFFError::NestingLimitReached);
@@ -952,7 +952,7 @@ fn zero_char_string_offset() {
         UInt8(top_dict_operator::CHAR_STRINGS_OFFSET as u8),
     ]);
 
-    assert!(cff::Table::parse(&data).is_none());
+    assert!(cff::Table::parse(&data, 1000).is_none());
 }
 
 #[test]
@@ -978,7 +978,7 @@ fn invalid_char_string_offset() {
         UInt8(top_dict_operator::CHAR_STRINGS_OFFSET as u8),
     ]);
 
-    assert!(cff::Table::parse(&data).is_none());
+    assert!(cff::Table::parse(&data, 1000).is_none());
 }
 
 // TODO: return from main