Most of the existing methods to solve the closest lattice point problem are based on an efficient search of the lattice points. In this paper, a novel alternative approach is suggested where the closest point to a given vector is found by calculating which Voronoi cell contains this vector in an iterative manner. Each iteration is made of simple "slicing" operations, using a list of the Voronoi relevant vectors that define the basic Voronoi cell of the lattice. The algorithm is guaranteed to converge to the closest lattice point in a finite number of steps. The method is suitable, for example, for decoding of multi-input multi-output (MIMO) communication problems. The average computational complexity of the proposed method is comparable to that of the efficient variants of the sphere decoder, but its computational variability is smaller.