A generalized tripartite scheme is proposed for splitting an arbitrary two-qubit state by utilizing six-qubit non-maximally cluster states as quantum channel. It was shown that the splitter averagely partitions its unknown two-qubit state between two agents and either agent can recover the unknown state with the other agent’s assistance via appropriate unitary operation. A generalized Bell state measurement (GBM) and a single-particle measurement (SM) are needed in the scheme. In order to obtain the original state, an auxiliary particle was introduced and a suitable entangled match was selected. The probability of the successful quantum-information splitting (QIS) and classical communication cost was worked out. If the quantum channel consists of maximally state, the classical information consumes 14 bits, and the total probability of QIS equals to 1.