We consider the problem of universal prediction of individual binary sequences where the universal predictor is a deterministic finite state machine with a fixed number of states. We examine the case of self-information loss, where the predictions are probability assignments. The performance of the predictors is measured by their redundancy w.r.t. the constant predictors class. We obtain an improved lower bound on the redundancy of any finite state (FS) predictor with K states. We construct a FS predictor based on the lower bound and compare the performance of the predictor to the lower bound. Numerical results show that the redundancy of the proposed FS predictor is close to that predicted by the lower bound.