The process of relaxation of a unidirectional magnetic field in a highly conducting tenuous fluid medium is considered. Null points of the field play a critical role in this process. During an initial stage of relaxation, variations in magnetic pressure are eliminated, and current sheets build up in the immediate neighborhood of null points. This initial phase is followed by a long diffusive phase of slow algebraic decay of the field, during which fluid is continuously sucked into the current sheets, leading to exponential growth of fluid density and concentration of mass around the null points, which show a tendency to cluster. Ultimately, this second phase of algebraic decay gives way to a final period of exponential decay of the field. The peaks of density at the null points survive as a fossil relic of the decay process. Numerical solution of the governing equations provides convincing confirmation of this three-stage scenario. Generalizations to two- and three-dimensional fields are briefly considered.