Measurements of the analyzing power for the pp-->pp eta reaction have been performed at excess energies of Q=10 and 36 MeV. The determined analyzing power is essentially consistent with zero, implying dominance of the s wave at both excess energies. The angular dependence of the analyzing power, combined with the isospin dependence of the total cross section for the eta meson production in nucleon-nucleon collisions, reveal that the excitation of the nucleon to the S11(1535) resonance is predominantly due to the exchange of the pi meson between the colliding nucleons.