The new method developed in this paper is aiming at transmission congestion management (CM). The new, Optimal Transactions Management method (OTM), is based on linear programming (LP), DC load flow (DCLF) and linear security constraints. The OTM method is embedded in Available Transfer Capabilities (ATCs) and Power Transfer Distribution Factors (PTDFs) definitions' environment. Well-suited for both preventive and corrective modes of operation, the OTM method aids transmission system operator in running a congested power system network, where congestions are due to transactions. Potential congestion threat is solved by finding the 'culprit' transaction and its optimal reduction. Besides the proposed downsizing of scheduled and/or committed transactions, controls of the OTM method also include redispatching of generation and load levels. The task is to establish a system state without constraint violations. To ensure the feasible network solution, both DC and AC power flows are used. The common 5 nodes/7 lines Ward&Hale sample power system is used to clarify the OTM method. Besides, six other power system networks including the real-life power system network of Serbia, Macedonia and Montenegro (part of the South East Europe - SEE grid) are used to test remedial potentials and CPU-time performances of the method. The 24-hour daily demand diagram is used with all test networks to study the effects of transactions as they are being superimposed to the regional grid. The remedial, transactions-curtailing OTM method is found well suited for market-related analyzes precluding the hour-ahead, the day-ahead dispatch, as well as the real-time generation dispatch. It could also suit for the novel, Day Ahead Congestion Forecast (DACF) procedure used in power markets.