The use of the Constant Modulus (CM) criterion to achieve blind equalization of Continuous Phase Modulated signals is investigated in this paper. Solutions to the CM criterion are characterized. It is shown that blind equalization using the CM criterion may be unsuccessful in the sense that the output of the equalizer does not necessarily coincides with a delayed and rotated version of the input signal. An indeterminacy indeed remains and this residual indeterminacy is characterized. As an application of our results, a blind equalization criterion which allows to eliminate the latter indeterminacy is proposed. Simulation results sustain theoretical claims and illustrate the attractive performance of the proposed criterion.