Abstract: The bidirectional steerability between different-size subsystems is discussed for a single parameter accelerated qubit–qutrit system. The decoherence due to the mixing and acceleration parameters is investigated, where for the total system and the qutrit, it increases as the mixing parameter increases, while it decreases for the qubit. The non-classical correlations are quantified by using the local quantum uncertainty, where the uncertainty increases at large values of the acceleration parameter. The possibility that each subsystem steers each other is studied, where the behavior of the steering inequality predicts that the qubit has a large ability to steer the qutrit. The degree of steerability decays gradually when the qubit is accelerated. However, it decays suddenly when the qutrit or both subsystems are accelerated. The degree of steerability is shown for the qutrit vanishes at small values of the acceleration, while the qubit at large acceleration. The difference between the degrees of steerability depends on the initial state settings and the size of the accelerated subsystem.