We study the adaptive decomposition of functions in the complex Hardy spaces (Formula presented.) by higher order Szegö kernels. The purpose is to treat signals that are essentially of high frequencies. We show that each kernel function (basic function) we use is either a mono-component (as an analytic signal, its instantaneous frequency is positive everywhere), or a sum of two orthogonal mono-components. The proposed decomposition thus belongs to the category of adaptive mono-component decomposition.