We proved a multiplicity result for strongly indefinite semilinear elliptic systems -Delta u + u = +/- 1/(1 + vertical bar x vertical bar(a))vertical bar v vertical bar(p-2)v in R(N), -Delta v + v = +/- 1/(1+vertical bar x vertical bar(b))vertical bar u vertical bar(q-2)u in R(N) where a and b are positive numbers which are in the range we shall specify later. Copyright (C) 2009 Kuan-Ju Chen.