The article is devoted to creation and justification of new statistical criterion of pairwise independence of binary sequences from given set, which are considered as realization of random variables. The corresponding algorithm, which fulfills the checking of pairwise independence, is formulated in details. This algorithm is necessary tool for statistical veri-fication of cryptographic quality of different cryptoprimitives, which functioning is con-nected with random/ pseudorandom sequences generation — such as ran-dom/pseudorandom sequences generators or stream ciphers. Usage of the obtained criteri-on allows independence checking not only for output sequences, but also for its interme-diate state or inputs. Note that such independence is necessary for unpredictability of out-put sequences.