This letter considers the estimation of modulation index for binary continuous phase modulated (CPM) partial response signals. The actual value of modulation index in low-cost implementations turns out to be different than the nominal value used at the transmitter, leading to severe performance degradation. One possible solution is the deployment of an estimation algorithm at the receiver. The proposed data-aided best linear unbiased estimator (BLUE) is based upon a linear model approximation of the differential phase of pre-averaged CPM signal. Theoretical analysis of the variance of the estimator is presented to establish its improved performance. Simulation results also corroborate significant improvement of the proposed estimator at lower signal-to-noise ratio (SNR) values as compared to existing estimators, while retaining the linear bound performance at high SNRs. We show that the bit error rate (BER) performance at low SNRs is also improved when the modified BLUE estimator is deployed at the receiver.