Separation of a ternary mixture into almost pure components is discussed. Systems of distillation columns with higher thermodynamic efficiency are developed from a direct sequence (or indirect sequence) of distillation columns by allowing for two interconnecting streams of the same composition and different enthalpy. This increases the reversibility of distillation in the second column, which results in replacing a portion of the high-temperature boiling duty with a lower-temperature heat in the direct split case. For the indirect split case, the improvement allows a portion of the low-temperature condensing duty to be replaced with a higher-temperature condensation.