In this letter, we first incorporate the concept of index modulation (IM) into simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided non-orthogonal multiple access (NOMA) system to improve the spectral efficiency. Specifically, the proposed IM aided STAR-RIS-NOMA system enables extra information bits to be transmitted by allocating subsurfaces to different users in a pre-defined subsurface allocation pattern. Furthermore, an approximate closed form expression on bit error rate (BER) is derived. Simulation results demonstrate that the proposed IM aided STAR-RIS-NOMA system is able to acquire transmission rate improvement compared to the conventional STAR-RIS NOMA.