A geometric (n 4 ) configuration is a collection of n points and n lines, usually in the Euclidean plane, so that every point lies on four lines and every line passes through four points. This paper introduces a new class of movable ((5m) 4 ) configurations-that is, configurations which admit a continuous family of realizations fixing four points in general position but moving at least one other point-including the smallest known movable (n 4 ) configuration.