A method of transferring funds electronically, is performed by a group of N computers X(1) thru X(N) which are intercoupled to each other, and to another computer Y, by a communication channel. Each computer of the group includes multiple customer accounts, and the computer Y includes a net account for each computer of the group. To initiate the transfer of funds between two customer accounts, a customer sends an input request to one of computers X(i) of the group; and this input request specifies that funds F(z) be transferred in a particular direction between a customer account A(r) in computer X(i) and a customer account A(s) in another computer X(j) of the group. For each input request that is received by computer X(i), a respective sequence of electronic control messages is sent on the communication channel among the computers X(i), X(j) and Y. By this sequence of control messages, computer X(i) tests the status of customer account A(r); computer X(j) tests the status of customer account A(s); and computer Y tests the status of the net accounts for computers X(i) and X(j). If all of the tests by the computers X(i) and x(j) are satisfied, then those computers both authorize computer Y to transfer the funds F(z) between the net accounts for computers X(i) and X(j); and if all of the tests by computer Y are satisfied, then computer Y authorizes the computers X(i) and X(j) to transfer the funds F(z) between the customer accounts A(r) and A(s). This authorization from all three computers eliminates the need to reverse a transfer of funds; and consequently, the transferred funds are available for withdrawal immediately after the sequence of messages is completed successfully.