Model reference adaptive control is a major design method for controlling plants with uncertain parameters. The primary objective of this paper is to develop a new design approach for a differentiator-free model reference adaptive control of a single-input single-output linear time-invariant plant. The proposed method, called the "Identifier-tracking model reference adaptive control", uses a stacked identifier structure that is new to the field of adaptive control. The goal is to make the output of the plant asymptotically track the output of the first identifier, and then driving the output of the first identifier to track that of the second identifier, and so forth, up to the qth identifier where q is the relative degree of the plant. Lastly, the output of the qth identifier is forced to converge to that of the reference model. Simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response. Since the resulting control systems are non-linear and time-varying, the stability analysis of the overall system plays a central role in developing the theory.