A novel method for reconstruction from highly undersampled parallel MRI data is proposed. The method computes the Stationary Wavelet Transform (SWT) of the unknown MR image directly from sub-sampled k-space measurements, and then recovers the image using the Inverse SWT filter bank. Experiments with in-vivo data show that this method produces high quality reconstructions, comparable to Compressed Sensing (CS) reconstructions. However, unlike CS, the proposed method is non-iterative. Moreover, it is simple, fast, and allows flexible (random or ordered) k-space undersampling schemes.