In radar signal processing, it is important to improve target detectability over various clutter which may be caused by a number of different sources. Frequently the location of these sources is additionally subject to variations in time and position, i.e., the output clutter level is not kept constant and discrimination of the target from clutter is no longer easy. This fact calls for adaptive signal processing technique operating in accordance to the local clutter situation. The present paper suggests such a technique. One advantage of this technique is that, over a wide class of no-signal environments, the false alarm rate remains the same. Also, no learning process is necessary in order to achieve the constant false alarm rate (CFAR). In this paper, a CFAR test is developed. The test is applicable to the detection of a signal in some elements of a multiple-resolution-element radar. It is based on the use of binary integration and the order statistics. Binary integration is a nonlinear process that counts the number of times the return signal from a given sequence exceeds a threshold (referred to as the first threshold). The new adaptive test (for discriminating targets from clutter), proposed here, utilizes the parameter- free statistics obtained from the above order statistics. These parameter-free statistics are transformed to the distribution-free statistic which is compared to another threshold (referred to as the second threshold) for the decision. The adaptive test is able to achieve a fixed PFA (probability of a false alarm) which is invariant to intensity changes in the noise background. The results of computer simulation are presented as an evidence of the validity of the theoretical predictions of performance of the suggested CFAR test.