Abstract: In order to reduce the broadening of output beam line width in negative-branch off-axis unstable resonator laser, the function relationship between the two main parameters of effective Fresnel number Neff and geometry magnification M and excess noise factor K of output mode was analyzed. From negative branch structure, excess noise factor was firstly presented as functional distribution of transverse mode in output plane based on classical wave equation theory. By using the edge wave method, output transverse mode was approximated as a function of Neff and M. And then, the dependence of K on Neff and M were numerical calculated. The results indicate that K changes quasi-periodically with Neff. The cyclical peak is presented at Neffs+0.85 (s is a positive integer). Output line width is broadened nearly 2000 times of the natural line width. The study is useful for the research of output loss of unstable resonator and provides reference for practical laser designs.