We introduce a new hybrid algorithm called the generalized sidelobe decorrelator (GSD) that combines elements of geometric beamforming and blind source separation. On the one hand, it is as an extension of the generalized sidelobe canceller (GSC), also known as the Griffiths-Jim beamformer, from the standard criteria of power minimization to a decorrelation criteria. On the other hand, it can be seen as an extension of a particular blind source separation (BSS) algorithm for non-stationary signals, to include prior information about the location of one of the sources. However, unlike GSC, it is capable of removing noise leakage into the primary beam and, unlike BSS algorithms, it performs well independent of whether the sources are simultaneously active. This makes it ideal for noise reduction in a continuously running on-line operation. We demonstrate its superior performance in a real-room audio experiment.