The code length of Tardos's collusion-secure fingerprint code is of theoretically minimal order with respect to the number of adversarial users (pirates). However, the constant factor should be further reduced for practical implementation. In this article, we improve the tracing algorithm of Tardos's code and propose a 2-secure and short random fingerprint code, which is secure against collusion attacks by two pirates. Our code length is significantly shorter than that of Tardos's code and its tracing error probability is practically small.