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The traditional CFAR processors are based on the sliding-window concept, which have substantial performance degradation under nonhomogeneity. Owing to temporal processing and the exploitation of the local homogeneity of the map cell, the clutter-map procedure acquires enhanced robustness with little CFAR losses. In this paper, a Gaussian biparametric clutter-map constant false alarm rate (GBCM-CFAR) processor is proposed which merges the clutter-map technique and noncoherent integration together. It can approximately achieve CFAR independent of the original clutter distribution. The performance in the presence of fast point targets is assessed, in the examples of Weibull and lognormal clutter, in order to elicit the effect of the system parameters. Its performance is close to that of the optimum Neyman-Pearson detector with little CFAR losses in homogeneous environments. It is also suitable to deal with the nonhomogeneous situation.