The "Model Reference Adaptive Control (MRAC)" is a popular approach from the early nineties to our days. Its basic idea is the application of proper feedback that makes the behavior of the controlled system identical to that of the "reference model". It has many particular variants with the common feature that they are designed by the use of Lyapunov's 2 nd method. Though this approach normally guarantees global asymptotic stability, its use can entail complicated parameter tuning process that is sensitive to unknown external disturbances. In this paper an alternative approach, the application of "Robust Fixed Point Transformations (RFPT)" in the MRAC technique is recommended. It applies strongly saturated, multiplicative nonlinear terms causing a kind of " deformation" of the input to the available imprecise system model. The appropriate "deformation" is obtained by Cauchy Sequences that are convergent only within a local basin of attraction. This technique can well compensate the simultaneous consequences of modeling errors and external disturbances, too. To stabilize the control within the range of convergence a simple tuning procedure is recommended in this paper, too. As a potential application paradigm the novel MRAC control of a "cart - beam - hamper" system is considered. The conclusions of the paper are illustrated by simulation results.