This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2 n for n-bit shift register with a nonlinear feedback function. The developed method is illustrated by constructing a nonlinear function feedback shift register. It is proved that the offered method requires the realization of a memory size proportional to n 2 that allows making successful use of suitable generators for practical use on the shift register of the longer word.