The students in molecular spectroscopy courses are often required to determine the permitted normal vibrations for linear molecules that belong to particular groups. The reducible group representations generated by the use of Cartesian coordinates can be reduced by the use of a simple algebraic process applied to the group representations. The method relies on the linear independence of the cosines of integral multiples of the rotation angle j. The systems of linear equations that arise can be solved readily by hand calculations, even in the most general cases. When compared with the results of standard textbook presentations, this approach is easy, efficient, and certain. This kind of process would appear to be extendible to other continuous groups.