We propose the use of the polar decomposition for the preconditioning of the one-sided block-Jacobi algorithm for the singular value decomposition of a given matrix A. The preconditioner comes from the eigenvalue decomposition of the Hermitian factor H, which is computed by using (partial) Halley’s iterations. This approach eliminates the computation of the Gram matrix \(A^TA\) , which is not numerically reliable for very ill-conditioned matrices A. The iterated matrix in Halley’s iterations has a special structure, and three variants for its QR decomposition are proposed and compared. Numerical experiments show, that this new approach is efficient for very ill-conditioned matrices, whereas the Gram matrix can be safely used in other cases.