This paper addresses the construction of a family of wavelets based on halfband polynomials. An algorithm is proposed that ensures maximum zeros at for a desired length of analysis and synthesis filters. We start with the coefficients of the polynomial and then use a generalized matrix formulation method to construct the filter halfband polynomial. The designed wavelets are efficient and give acceptable levels of peak signal-to-noise ratio when used for image compression. Furthermore, these wavelets give satisfactory recognition rates when used for feature extraction. Simulation results show that the designed wavelets are effective and more efficient than the existing standard wavelets.