In this paper

we describle a fast

stable algorithm for solving symmetric inde-finite systems of linear equations Ax=b

the main idea of which is to take full advantage of the symmetry and few positive (or negative) eigenvalues of A.The number of operations involved in the algorithm are n3/6+O(n2) multiplications and additions

and n2/2+O(n) storages are needed.From the examples given in 4

this algorithm is better than the algorithm provided by Parlett and Reid in above hypothsis

it is more effective that A is a Iarge matrix.