To develop an improved reconstruction method, k-space subtraction with phase and intensity correction (KSPIC), for highly accelerated, subtractive, non-contrast-enhanced MRA. The KSPIC method is based on k-space subtraction of complex raw data. It applies a phase-correction procedure to restore the polarity of negative signals caused by subtraction and an intensity-correction procedure to improve background suppression and thereby sparsity. Ten retrospectively undersampled data sets and 10 groups of prospectively undersampled data sets were acquired in 12 healthy volunteers. The performance of KSPIC was compared with another improved reconstruction based on combined magnitude subtraction, as well as with conventional k-space subtraction reconstruction and magnitude subtraction reconstruction, both using quantitative metrics and using subjective quality scoring. In the quantitative evaluation, KSPIC had the best performance in terms of peak SNR, structural similarity index measure, contrast-to-noise ratio of artery-to-background and sharpness, especially at high acceleration factors. The KSPIC method also had the highest subjective scores for all acceleration factors in terms of vessel delineation, image noise and artifact, and background contamination. The acquisition can be accelerated by a factor of 20 without significant decreases of subjective scores. The optimal size of the phase-correction region was found to be 12-20 pixels in this study. Compared with combined magnitude subtraction and conventional reconstructions, KSPIC has the best performance in all of the quantitative and qualitative measurements, permitting good image quality to be maintained up to higher accelerations. The KSPIC method has the potential to further reduce the acquisition time of subtractive MRA forclinicalexaminations.