In this work, we present a novel cortical correspondence method with application to the macaque brain. The correspondence method is based on sulcal curve constraints on a spherical deformable registration using spherical harmonics to parameterize the spherical deformation. Starting from structural MR images, we first apply existing preprocessing steps: brain tissue segmentation using the Automatic Brain Classification tool (ABC), as well as cortical surface reconstruction and spherical parametrization of the cortical surface via Constrained Laplacian-based Automated Segmentation with Proximities (CLASP). Then, initial correspondence between two cortical surfaces is automatically determined by a curve labeling method using sulcal landmarks extracted along sulcal fundic regions. Since the initial correspondence is limited to sulcal regions, we use spherical harmonics to extrapolate and regularize this correspondence to the entire cortical surface. To further improve the correspon- dence, we compute a spherical registration that optimizes the spherical harmonic parameterized deformation using a metric that incorporates the error over the sulcal landmarks as well as the normalized cross correlation of sulcal depth maps over the whole cortical surface. For evaluation, a normal 18-months-old macaque brain (for both left and right hemispheres) was matched to a prior macaque brain template with 9 manually labeled, major sulcal curves. The results show successful registration using the proposed registration approach. Evaluation results for optimal parameter settings are presented as well.