<p>In this paper, we establish the generic <i>R</i>-linear convergence of an improved proximal polar decomposition algorithm (iPPDA) for the symmetric low rank orthogonal tensor approximation problem. For this purpose, the map from the parametrization space to the set of symmetric low rank orthogonally decomposable tensors is studied. We show that there is a natural stratification of the set of symmetric low rank orthogonally decomposable tensors, and there is a local diffeomorphism from the parametrization manifold to the smooth part of the set of symmetric low rank orthogonally decomposable tensors. As a result, properties of the Euclidean projection onto a manifold via Morse theory can be employed, and the generic <i>R</i>-linear convergence can be shown.</p>