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In this article two new types of wavelet bases for Hermite quintic splines are offered. The algorithm of wavelet decomposition as the solution of three systems of the linear equations, from which one system is three-diagonal with strict diagonal domination and two other systems are four-diagonal, is received.doi:10.13189/ujcmj.2013.010401 fatcat:gt65tzkdpza4hlzvmx6wngucsy