The proposed scheme by Domingo in Electronic Letters presented the first anonymous fingerprinting scheme in which help of a registration center is not required in order to identify redistributors. However, registration protocol of this scheme is 4-pass and identification process also required many exponential operations. In this paper, we propose more efficient protocol than the scheme by Domingo, which require 2-pass in registration protocol and need only 3+1 times exponential operation in identification process. In the electronic commerce of digits contents, registration protocol is more efficient than the previous scheme introduced. Moreover, computational complexity is diminished since identification process requires only 3+1 times exponential operation as the previous one requires 3+N/2 exponential operations. We now show efficient anonymous fingerprinting of electronic information with improved automatic identification of redistributors.