Using the projection method for frames [\textit{O. Christensen}, Appl. Comput. Harmon. Anal. 1, No. 1, 50-53 (1993; Zbl 0849.42025)] this paper gives two equivalent conditions for a frame to be a Riesz basis in a separable Hilbert space. These conditions emerge from taking the limit in a sequence of nested finite dimensional subspaces. As a bonus, expressions for the Riesz bounds are obtained by taking the limit for the Riesz bounds of the finite dimensional subspaces. These can be expressed in terms of the largest and smallest eigenvalues of the Gram matrix of these subspaces.