Bounds, analogous to the classical bounds of J. H. Wilkinson [Numer. Math. 4, 296-300 (1962; Zbl 0104.345)] and H. P. M. Van Kempen [Numer. Math. 9, 19-22 (1966; Zbl 0229.65038)] for the Jacobi method for the symmetric eigenvalue problem, are proved which establish the quadratic convergence of the “serial singular value decomposition Jacobi” (or “Kogbetliantz”) method for triangular matrices. The results apply in the case of multiple singular values which are not clustered.