We study a heuristic modification of the NESTA algorithm for compressed sensing reconstruction of TOF-MRA images, where at each iteration the calculated k-space data are replaced with the original (acquired) data wherever the latter are available. We compared the modified method with the original method. In qualitative visual analysis, reconstructed images from the modified method were a little noisier but with better vessel signal delineation. In quantitative analysis, the modified method as compared with the original method marked higher rVBR values in lower sampling ratio, and caused no image degradation in higher sampling ratio. The modified method therefore provides a viable option in improving reconstruction of the NESTA algorithm for TOF-MRA undersampled data.