The CMS detector is designed around a large 4 T superconducting solenoid, enclosed in a 12 000-tonne steel return yoke. A detailed map of the magnetic field is required for the accurate simulation and reconstruction of physics events in the CMS detector, not only in the inner tracking region inside the solenoid but also in the large and complex structure of the steel yoke, which is instrumented with muon chambers. Using a large sample of cosmic muon events collected by CMS in 2008, the field in the steel of the barrel yoke has been determined with a precision of 3 to 8% depending on the location.