A strong, uniform electric field was used to achieve brute force orientation of supersonically cooled cyanogen bromide. Laser-induced fluorescence of the CN fragment from photolysis of the sample at 213 nm was detected. A 20% enhancement in signal was observed when the dissociation laser was polarized parallel, rather than perpendicular, to the orientation field. This indicates the dominance of a transition dipole moment parallel to the permanent dipole of the molecule. However, the degree of enhancement falls well below that predicted for a pure parallel transition at a rotational temperature of 1.5 K. Thus, evidence of contribution from a perpendicular transition is seen. Based on quantitative analysis, the direction of the effective transition dipole, and thereby the amount of contribution from a transition dipole perpendicular to the permanent dipole of the molecule, can be determined. Using this method, approximately 33% perpendicular character was found in the dissociation process of BrCN at 213 nm.