A new algorithm for reconstructing a signal from its wavelet transform modulus maxima is presented based on an iterative method for solutions to monotone operator equations in Hilbert spaces. The algorithm’s convergence is proved. Numerical simulations for different types of signals are given. The results indicate that compared with Mallat’s alternate projection method, the proposed algorithm is simpler, faster and more effective. A new algorithm for reconstructing a signal from its wavelet transform modulus maxima is presented based on an iterative method for solutions to monotone operator equations in Hilbert spaces. The algorithm’s convergence is proved. The simulations for different types of signals are given. The results indicate that Compared with Mallat’s alternate projection method, the proposed algorithm is simpler, faster and more effective.