Time-Triggered Ethernet (TTE) for aeronautical and astronautical applications places stringent requirements on real-time communication and message security.Efficient global static scheduling technology is conducive to fully guaranteeing the service quality of different messages.Considering that the Time-Triggered (TT) messages with the highest real-time performance determine the transmission time of low-priority Rate-Constrained (RC) messages, a TTE optimal scheduling technology based on rapid increment is proposed.By rapidly incrementing the basic scheduling unit, backtracking to correct the multi-hop delay, and optimizing the static schedule of TT messages, the transmission performance of RC messages is improved.Finally, the network scheduling algorithm is applied to the network topology model of the time-triggered avionics system for verification.The simulation experiment shows that the TTE optimal scheduling technology effectively improves the real-time performance of the network under the condition that the TT messages satisfy the transmission constraints.The average end-to-end latency of RC messages is optimized by 14.08%, and the worst end-to-end latency is optimized by 22.86%.