This paper will present a new algorithm for determining the presence or absence of a weak signal in non-Gaussian noise. A weak signal is one that is vanishingly small compared to the noise disturbance. There are several applications in which detecting a weak signal is important. If the weak signal is the result of the reflection of a small target then accurate detection can indicate target presence. If the target is maneuvering and measurements can only be made at widely separated fixed intervals, then after target detection an estimate of target velocity can be made. The algorithm presented in this paper is no more structurally complex than the LOD, yet possesses several important advantages over the LOD. The fundamental advantage is the fact that the underlying noise statistics do not have to be known a prior. In addition, whereas the LOD may require a rather complex nonlinearity to preprocess the data, the algorithm presented here does not. This paper will develop the algorithm, and then report on simulation testing that was performed to ascertain its performance. It will be shown that the proposed algorithm performs significantly better (that is, is able to detect the presence of weak targets) than more conventional linear detection methods (Wiener filtering).