Motivated by the recent growing interest in pairwise learning problems, we study the generalization performance of Online Pairwise lEaRning Algorithm (OPERA) in a reproducing kernel Hilbert space (RKHS) without an explicit regularization. The convergence rates established in this paper can be arbitrarily closed to O(T−12) within T iterations and largely improve the existing convergence rates for OPERA. Our novel analysis is conducted by showing an almost boundedness of the iterates encountered in the learning process with high probability after establishing an induction lemma on refining the RKHS norm estimate of the iterates.