In order to get a well reliability parameter, a new daughter wavelet for phase reconstruction of optical carrier-fringe pattern was proposed. The phase of the fringe pattern can be reconstructed from the ridge of the wavelet transform by employing this new daughter wavelet. The modulus of the new wavelet transform coefficients include both the modulation information and fringe density information, which can be treated as a well reliability parameter representing the phase reconstruction. Rigorous mathematical demonstration of this method was given. Theoretical demonstration shows that the modulus can be treated as a reliability parameter of the phase reconstruction. Computer simulation and experiment verify the feasibility of the proposed method.