Abstract: A method for effecting payments is suggested which allows protecting the financial interests of each participant of a payment during payments via open telecommunication nets from other participants' cheating, provides protection of the payers' and payees' privacy, admits payments ranging from micro-payments to business-to-business payments, ensures that the time taken to effecting a payment depends only on the speed of action of the net connections and not on the payment amount, makes it possible to serve of serving a number of clients which grows proportionally to the payment system operators resources, is easy to build into an arbitrary trade system, enables each client both to pay and to receive payments, and makes possible payments between clients of different banks. The method of effecting payments is realized with the help of programming means.