The aim of this article is to present a refined convergence theory of the SQPmethod applied to optimal control problems for the nonstationary Navier - Stokes equations. We will employ a second-order sufficient optimality condition, which requires that the second derivative of the Lagrangian is positive de. nite on a subspace of inactive constraints. Therefore, we have to use the Lp- theory of optimal controls of the nonstationary Navier - Stokes equations rather than Hilbert space methods. Estimates of state and adjoint equations with respect to Lp- norms are provided. Finally, the local convergence of the SQP- method is confirmed by numerical tests.