Computing the Lempel-Ziv Factorization (LZ77) of a string is one of the most important problems in computer science. Nowadays, it has been widely used in many applications such as data compression, text indexing and pattern discovery, and already become the heart of many file compressors like gzip and 7zip. In this paper, we show a linear time algorithm called Xone for computing the LZ77, which has the same space requirement with the previous best space requirement for linear time LZ77 factorization called BGone. Xone greatly improves the efficiency of BGone. Experiments show that the two versions of Xone: XoneT and XoneSA are about 27% and 31% faster than BGoneT and BGoneSA, respectively.