A uniform square spot lens is designed by the supporting quadratic method (SQM) and an algorithm for the interpolation and reconstruction of the curved surfaces based on the Zernike polynomials is developed. The mapping conservation points are chosen on the initial base surface for each sub-surface and the 9-point system is partitioned according to the adjacency relationship. As for this 9-point system, the linear equation group is established by using the lower order terms included in the polynomials and the partial curved surface is constructed with its unique solution. All the partial curved surfaces are spliced together and thus a complete and continuously smooth curved surface is obtained. This algorithm can simplify the later optimization of the initial base surfaces in SQM to a certain extent, which can ensure a good design effect of the uniform square spot lens.