This paper deals with the topic of an indirect carrier frequency offset estimation and elimination. The main goal is to modify a conventional method as an attempt to develop a different approach and then to compare the performance of the modified method with the performance of the conventional one. The conventional approach is here represented by the gradient optimization method called the steepest descent. It is the base for the modification which utilizes Newton's method for the indirect carrier offset estimation. Both algorithms are implemented as phase-locked loops in a model of communication system. The simulation is processed in Matlab.