The search for signatures of transient, unmodelled gravitational-wave (GW) bursts in the data of ground-based interferometric detectors typically uses 'excess-power' search methods. One of the most challenging problems in the burst data analysis is to distinguish between actual GW bursts and spurious noise transients that trigger the detection algorithms. In this paper, we present a unique and robust strategy to 'veto' the instrumental glitches. This method makes use of the phenomenological understanding of the coupling of different detector sub-systems to the main detector output. The main idea behind this method is that the noise at the detector output (channel H) can be projected into two orthogonal directions in the Fourier space—along, and orthogonal to, the direction in which the noise in an instrumental channel X would couple to H. If a noise transient in the detector output originates from channel X, it leaves the statistics of the noise component of H orthogonal to X unchanged, which can be verified by a statistical hypothesis testing. This strategy is demonstrated by doing software injections in simulated Gaussian noise. We also formulate a less rigorous, but computationally inexpensive alternative to the above method. Here, the parameters of the triggers in channel X are compared to the parameters of the triggers in channel H to see whether a trigger in channel H can be 'explained' by a trigger in channel X and the measured transfer function.