In the HEVC standard, UIP (unified intra prediction) is included as one of the new coding tools in the latest HM software, which supports 33 different directions in addition to the DC prediction mode. It represents directional structures more accurately, and performs remarkable bit rate saving. However, UIP also significantly increases the burdens on computational complexity. This contribution proposes a reversed intra prediction which utilizes the inherent correlation between luma and chroma. By reversing the prediction orders, the chroma prediction is executed first in order to create the depth map and mode candidate subset that will reduce the computational complexity in luma intra prediction. Experiment results show that the proposed algorithm can achieve approximately 30% time savings in average with 0.03, 0.05 BD-PSNR losses in chroma components and unnoticeable increments in bit rate.