Commonly used methods for estimation of a seamount's magnetization parameters directly from its observed magnetic anomaly assume uniform magnetization amplitude and direction throughout the seamount. We approximate seamount bathymetry by a set of stacked rectangular prisms. Definition of the magnetization vector in terms of its amplitude and direction, instead of its three Cartesian components, is then used to separately estimate the magnetization amplitude of each component prism and their common magnetization direction by the iterative algorithm of Marquardt. Therefore, the magnetization properties of a seamount can be estimated under the assumptions of uniform magnetization direction and nonuniform magnetization amplitude within the seamount. A theoretical example shows that the method can have good resolution in determining magnetization direction. A field example, already extensively studied by Harrison under the assumption of a uniform magnetization vector, shows that the method can be successfully applied to observed data.