The Flexible Time-Triggered communication over Switched Ethernet protocol (FTT-SE) was proposed to overcome the limitation of guaranteeing the real-time communication requirements of conventional switches, and at the same time to support reconfiguration of dynamic adaptive systems. The protocol fragments large messages into a sequence of packets that are individually scheduled. The maximum transmission unit (MTU), that restricts the packets size, has a significant effect on the schedulability of the packets. In this paper, we investigate the problem of selecting the optimal MTU size that maximizes the schedulability of real-time messages. We propose two algorithms to find optimal/sub-optimal values of MTU; the first one finds an optimal solution but exhibits high computational complexity, while the second one is sub-optimal but exhibits a lower computational complexity. Finally, we evaluate our proposed algorithms by means of simulation studies and compare their results with the results of assigning MTU to the maximum packet size that the protocol can allow.