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In this paper, direct torque control (DTC) algorithms for a split-phase induction machine (SPIM) are established. An SPIM has two sets of three-phase stator windings, with a shift of thirty electrical degrees between them. The significant contributions of this paper are: 1) two new methods of DTC technique for an SPIM are developed, called Resultant Flux Control Method and Individual Flux Control Method and 2) advantages and disadvantages of both methods are discussed. High torque ripple is a disadvantage for three-phase DTC. It is found that torque ripple in an SPIM can be significantly reduced without increasing the switching frequency.