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Starting from an extension of Kaczmarz's method, obtained by us in a previous paper, we introduce new directions for projections. We prove that by this, we don't modify the set of limit points of the original extended Kaczmarz algorithm. For the class of boundary value problems or integral equations of the first kind, we describe a method for constructing these new directions. It is based on considering coarser level of discretization for the initial problem. Some numerical experiments are also presented.