Although CPA (canonical/parallel factor analysis) has a unique solution, the actual computation can be made more robust by incorporating extra constraints. In several applications, the factors in one mode are known to be statistically independent. On the other hand, in Independent Component Analysis (ICA), it often makes sense to impose a Khatri-Rao structure on the mixing vectors. In this paper, we propose a new algorithm to impose independence constraints in CPA. Our algorithm implements the algebraic CPA structure and the property of statistical independence simultaneously. Numerical experiments show that our method outperforms in several cases pure CPA, pure ICA, and tensor ICA, a previously proposed method for combining ICA and CPA. We also present a strategy for imposing full or partial symmetry in CPA.