The concept of nonlocality and its role in the violation of Bell's inequalities (BI) are discussed. A weaker nonlocality is revealed in comparison with Albert Einstein's "Spooky Action at a Distance" and at the same time does not contradict the principles of the special theory of relativity (STR). A correlation statistical experiment with the violation of the Clauser—Horne—Shimony—Holt (CHSH) inequality in STR is described, in which weak nonlocality is manifested. The correlation in such an experiment propagates with infinite speed in the proper frame of reference of the measuring device.