In this talk, we will present three results on the convergence rate of the higher order power method (HOPM) for finding the best rank one approximation of a real tensor. They are: (i) the global sublinear convergence rate under all initializations, (ii) the R-linear convergence for a generic tensor under all initializations, and (iii) the R-linear convergence for an orthogonally decomposable tensor under all initializations. The key ingredient is by showing the non-degeneracy of all the singular vector tuples of a generic tensor and that of all the nonzero singular vector tuples of an orthogonally decomposable tensor.