Summary: By analyzing the characters of thermo field dynamics, which is proposed by Takahashi and Umezawa, we find that a new physical state, named the thermo-invariant coherent state, should exist in thermal equilibrium. This state not only maintains the whole energy of the system and the reservoir but is also a coherent state. We find its explicit form, its relation to the thermal coherent state and the thermal entangled state. When the whole system is in this state, annihilating a quantum of the system and in the meanwhile annihilating a hole with negative energy in the reservoir will not change the whole energy.