In this paper, the unsteady boundary-layer flow over a semi-infinite flat plate is solved by means of an analytic approach. Via an ad hoc technique based on the boundary-layer flow evolution, an analytic expression of the velocity profile is proposed. The proposed formula verifies well the results given by Rayleigh, Blasius, and Williams–Rhyne for all time, thus for all Strouhal number values, which is the characteristic of the studied problem. As the main results, the local skin friction depending on a Strouhal number is given in an aim to show an explanation on the flow evolutions from the initial solution to the steady solution in the whole spatial region. This approach permits us to take many applications in engineering technology when the analytic expressions of the velocity, temperature, and matter are looked for.