In this paper, we present a new lifting algorithm for triangular sets over power series. Our contribution is to give, for any power series triangular set, a shifted algorithm of which the triangular set is a fixed point. Then we can apply the relaxed recursive power series framework and deduce a relaxed lifting algorithm for this triangular set. We compare our algorithm to the existing techniques. Our algorithm always improves the asymptotic cost in the precision for the special case of univariate representations.