One-dimensional filtration at a rate which decreases hyperbolically, based on the Mints model [1], is considered. The system of model equations with the appropriate initial and boundary conditions is shown to be equivalent to the Goursat problems for hyperbolic equations. This is solved by the Riemann method using a method for finding a Riemann function proposed here. The method gives the well-known results for filtration at a constant rate. The hyperbolic and linear laws of filtration at a decreasing rate are shown to be equivalent under practical conditions of filter use.