Expressions are derived for determining the angular variation in the intensity of the forbidden hyperfine transitions ( Delta M=1, Delta m=+or-2) in the EPR spectra of transition ions. The intensities calculated using these expressions are compared with the predictions of Bleaney and Rubins and of Bir. It is found that third-order contributions arising from the nuclear spin operator as well as the quadrupole term are important in interpreting the intensity of forbidden hyperfine lines.