The problem of global adaptive stabilisation by state-feedback is investigated for a class of high-order non-linear systems with uncertain control coefficients and zero dynamics. First, some appropriate unknown parameters are introduced to obtain the updating laws when adapting control design. Then, by the flexible way of combining adding a power integrator with adaptive technique and the idea of changing supply functions, the requirement on the uncertain control coefficients is relaxed, and a recursive design procedure is successfully developed to achieve a continuous adaptive stabilising controller. Finally, an example is provided to illustrate the correctness of the theoretical results.