This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Omega of output function is given. As long as output function belongs to any closed sector included in Omega, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.