This paper is devoted to the design of a neural alternative to binary detectors optimized in the Neyman-Pearson sense. These detectors present a configurable low probability of classifying binary symbol 1 when symbol 0 is the correct decision. This kind of error, referred in the scientific literature as salse-positive or false alarm probability has a high cost in many real applications as medical Computer Aided Diagnosis or Radar and Sonar Target Detection, and the possibility of controlling its maximum value is crucial. The novelty and interest of the detector is the application of a Multilayer Perceptron instead of a classical design. Under some conditions, the Neural Detector presents a performance competitive with classical designs adding the typical advantages of Neural Networks. So, the presented Neural Detectors may be considered as an alternative to classical ones.