Using a resonance isobar model and an effective Lagrangian approach, from recent BES results on J/psi ->(p) over barp eta and psi ->(p) over barK(+)Lambda, we deduce the ratio between effective coupling constants of N-*(1535) to K Lambda and p eta to be R equivalent to g(N)(*)(1535)K Lambda/g(N)(*)(1535)p eta=1.3 +/- 0.3. With the previous known value of g(N)(*)(1535)p eta, the obtained new value of g(N)(*)(1535)K Lambda is shown to reproduce recent pp -> pK(+)Lambda near-threshold cross section data as well. Taking into account this large (NK)-K-* Lambda coupling in the coupled channel Breit-Wigner formula for the N-*(1535), its Breit-Wigner mass is found to be around 1400 MeV, much smaller than the previous value of about 1535 MeV obtained without including its coupling to K Lambda. The implication on the nature of N-*(1535) is discussed.