In this paper, a new non data-aided estimator of the modulation index of continuous phase modulated (CPM) signals is proposed. It is based on the observation that the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a sinusoid of period 2T, where T is the symbol period. The asymptotic behavior of the estimator is studied. If N is the sample size, the estimation error is shown to converge to a non-Gaussian distribution at a rate of 1/N. Simulation results sustain the conclusions of the theoretical asymptotic analysis.