We propose a new head-related transfer function (HRTF) interpolation method using Isomap, a nonlinear dimensionality reduction technique. First, we construct a single manifold for all subjects across both azimuth and elevation angles through the construction of an intersubject graph (ISG) that includes important prior knowledge of the HRTFs such as correlations across individuals, directions, and ears. Then, for a new direction, we predict its corresponding low-dimensional HRTF by interpolating over same subject low-dimensional measured HRTFs. Finally, we use a local neighborhood mapping in the manifold to reconstruct the high-dimensional HRTF from measured HRTFs of all subjects. We show that a single manifold representation obtained through the ISG is a powerful way to allow measured HRTFs from different subjects to contribute for reconstructing the HRTFs for new directions. Moreover, our results suggest that a small number of spatial measurements capture most of acoustical properties of HRTFs. Finally, our approach outperforms other linear and nonlinear dimensionality reduction techniques such as principal component analysis, locally linear embedding, and Laplacian eigenmaps.