The study of universal detector for fingerprinting code is strongly dependent on the design of scoring function. The optimal detector is known as MAP detector that calculates an optimal correlation score for a given single user's codeword. However, the knowledge about the number of colluders and their collusion strategy are inevitable. In this paper, we propose a new scoring function that equalizes the bias between symbols of codeword, which is called bias equalizer. We further investigate an efficient scoring function based on the bias equalizer under the relaxed marking assumption such that white Gaussian noise is added to a pirated codeword. The performance is compared with the MAP detector as well as some state-of-the-art scoring functions.