A fast decoding algorithm is described for the class of flexible coded-aperture designs introduced by Gourlay and Young [Appl. Opt.23, 4111 (1984)APOPAI0003-693510.1364/AO.23.004111]. The algorithm significantly reduces the number of mathematical operations required to perform the decoding of images produced using these apertures compared to currently known methods, such as direct decoding, and hence speeds up the image reconstruction. Experimental tests confirm the efficacy of the fast decoding algorithm, which offers a speed-up enabling a typical 120×120 element aperture to be decoded in around 1% of the time required for direct decoding.