A new gridding-based algorithm for stability analysis of Linear Parameter-Varying (LPV) systems is presented. The algorithm inherits the main features of classical gridding techniques: it can handle a vast class of parametric dependencies as well as non-convex parametric domains. Novelty of the proposed approach lies in the use of Haar wavelet transform theory to guarantee constraint satisfaction over the entire parametric domain, even for an arbitrarily sparse grid. It represents a major improvement over traditional gridding approaches, which fail to provide such a certificate without requiring a posteriori verification tests. The resulting algorithms rely on semidefinite programing and are related to sufficient stability conditions whose degree of conservatism decreases as the grid density and the Haar truncation level increase. Two numerical examples corroborate the validity of the proposed algorithms.