Pulse singularities with variable amplitudes appear in the corresponding positions of ignition coil primary current waveform when insulation fault occurs during the ignition process. We propose an algorithm to detect the singularities in ignition coil primary current signal. First calculate the multiscale continuous wavelet transform of the fault signal. Then pursue modulus maxima from the coarsest scale to the finest scale along the links between the adjacent scales. The pursue method avoids that the distribution characterization of modulus maxima on the modulus maxima map affects the detection outcome. Last draw the modulus maxima lines and determine the locations of the singularities. The results of experiments show that it has approximate computational complexity with the traditional modulus maxima singularity detection algorithm. In addition the algorithm has less error than traditional algorithm and some more complicated algorithms on identifying the singularities' location...