The Bayesian test with 0—1 loss function is a standard solution to solve a multiple hypothesis testing problem in the Bayesian framework. For a large number of applications (like the intrusion detection, the anomaly detection,…) the alternative hypotheses have quite different importance and 0—1 loss function does not reflect the reality. The quadratic loss function can be more appropriate to distinguish the concurrent hypotheses. The main contribution of the paper is the design of the Bayesian test with a quadratic loss function and its asymptotic study. When the signal-to-noise ratio tends to infinity, it is theoretically established that the error probabilities of the proposed test coincide with the error probabilities of the standard one associated to the 0—1 loss function. In the non-asymptotic case, the numerical experiments show that the proposed test outperforms the Bayesian test associated to the 0—1 loss function when compared by using the quadratic loss function.