As we reported previously, learning of a multi-layered hard-limited perceptron can be formulated into a set of simultaneous linear inequalities. Solving these inequalities under a given training set would then allow us to achieve the goal of learning in this system. If the dimension N of the input vector is much larger than the number M of different patterns to be learned, then there is considerable freedom for the system to select a proper solution of the connection matrix. In most cases, even a single layer perceptron will do the learning satisfactorily. This paper reports the results of some theoretical and experimental studies of this one-layered, hard-limited perceptron trained under the novel, one-step, noniterative learning scheme. Particularly, the analysis of some important properties of this novel learning system, such as automatic feature competition, domain of convergence, and robustness of recognition, are discussed in detail.