This paper describes a three-winding transformer protective relaying algorithm based on the ratio of increments of flux linkages (RIFL). To minimize the approximation errors, the algorithm uses integration approximation. The RIFL of the two windings is equal to the turns ratio for all operating conditions except for an internal fault. For a single-phase and three-phase transformer containing the wye-connected windings, the increments of flux linkages (IFL) are calculated. For a three-phase transformer containing the delta-connected windings, the difference of IFL between the two phases are calculated to use the line currents, because the winding currents are practically unavailable. Their ratios are compared with the turns ratio. The comparative study between the proposed and differential approximation methods was conducted. The test results show that the algorithm can reduce the errors resulting from the conventional methods.