Accurately corresponding a population of human cortical surfaces provides important shape information for the diagnosis of many brain diseases. This problem is very challenging due to the highly convoluted nature of cortical surfaces. Pairwise methods using a fixed template may not handle well the case when a target cortical surface is substantially different from the template. In this paper, we develop a new method to organize the population of cortical surfaces into pairs with high shape similarity and only correspond such similar pairs to achieve a higher accuracy. In particular, we use the geometric information to identify colocated gyri and sulci for defining a new measure of shape similarity. We conduct experiments on 40 instances of the cortical surface, resulting in an improved performance over several existing shape-correspondence methods.