Semi-grant-free (SGF) transmission has recently received significant attention due to its capability to accommodate massive connectivity and reduce access delay by admitting grantfree users to channels which would otherwise be solely occupied by grant-based users. In this paper, a new SGF transmission scheme that exploits the flexibility in choosing the decoding order in non-orthogonal multiple access (NOMA) is proposed. Compared to existing SGF schemes, this new scheme can ensure that admitting the grant-free users is completely transparent to the grant-based users, i.e., the grant-based users’ quality-of-service experience is guaranteed to be the same as for orthogonal multiple access. In addition, compared to existing SGF schemes, the proposed SGF scheme can significantly improve the robustness of the grant-free users’ transmissions and effectively avoid outage probability error floors. To facilitate the performance evaluation of the proposed SGF transmission scheme, an exact expression for the outage probability is obtained and an asymptotic analysis is conducted to show that the achievable multi-user diversity gain is proportional to the number of participating grant-free users. Computer simulation results demonstrate the performance of the proposed SGF transmission scheme and verify the accuracy of the developed analytical results.