Anewalgorithm of the minimum zone method for evaluating form error-the valid characteristic point method with the rapidly contracted constraint zone-is put forward in this paper. Its mathematical model is established and its fundamentals are illustrated in detail, also its process of computation is described. The essence of this new algorithm is to search out the geometric characteristic parameters of the enveloping feather of the minimum zone, such as the normal vectors of the enveloping planes for flatness error and the coordinates of the center of the enveloping circle for roundness error. Based on searching for the characteristic points by applying the judging criteria of the minimum zone, the new algorithm sets up automatically a constraint zone of the geometric characteristic parameters of the enveloping feathers of the minimum zone and contracts it rapidly. This algorithm searches the geometric characteristic parameter of the enveloping feather of the minimum zone efficiently and can iterate the minimum value of the form error quickly. A large number of examples indicate that this new algorithm has many advantages such as a high proportion of success in first searching, fast calculation speed and few turns of iteration. Also, it can be applied to a computer-assisted instrumentation system on line.