Characteristic pairs consist of lexicographical Groebner bases and the minimal triangular sets, called W-characteristic sets, contained in them, and they are good representations of multivariate polynomial ideals in terms of Groebner bases and triangular sets simultaneously. In this paper, we study how to decompose a polynomial set of arbitrary dimension into characteristic pairs with simple W-characteristic sets, and two algorithms are proposed over fields of zero characteristics and over finite fields respectively. Both of the algorithms rely on the concept of strong regular characteristic divisors, and the one for zero-characteristic fields also uses Lazard Lemma to test whether an ideal is radical. Experimental results are presented to illustrate the effectiveness of the proposed algorithms.