We study decomposition of functions in the Hardy space H2(D) into linear combinations of the basic functions (modified Blaschke products) in the system where the points an's in the unit disc D are adaptively chosen in relation to the function to be decomposed. The chosen points an's do not necessarily satisfy the usually assumed hyperbolic non-separability condition, in the traditional studies of the system. Under the proposed procedure functions are decomposed into their intrinsic components of successively increasing non-negative analytic instantaneous frequencies, whilst fast convergence is resumed. The algorithm is considered as a variation and realization of greedy algorithm.