This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.