An algorithm for determining the triangular decomposition H = R ∗ D R H = {R^ \ast }DR of a Hankel matrix H using O ( n 2 ) O({n^2}) operations is derived. The derivation is based on the Lanczos algorithm and the relation between orthogonalization of vectors and the triangular decomposition of moment matrices. The algorithm can be used to compute the three-term recurrence relation for orthogonal polynomials from a moment matrix.