The quantum coherence (QC) of two comoving atoms on a stationary trajectory is investigated. We develop a formalism to characterize the properties of atoms on a stationary trajectory. We give a criterion under which QC is frozen to a nonzero value. The frozen condition that vanishing super- or subradiant decay rate is not so sensitive to the initial condition of state. We show that enhanced QC and a subradiant state can be gained from the initial state.