The directional intra prediction (DIP) modes in HEVC are capable of predicting local continuous image features. Recently, intra block copy (IBC) is proposed for screen content coding, aiming at predicting non-local recurrent image features. For natural video, we observe that recurrent features are often irregular and not aligned with blocks. Thus, we propose a combination of DIP and IBC with block partition for better intra prediction, where one block can be divided into several partitions, each of which may choose between DIP and IBC. We study an intra prediction scheme with the proposed combination, especially the rate-distortion optimization and entropy coding in the scheme. Preliminary experimental results show that the proposed combined intra prediction achieves as high as 5.8% bit-rate saving compared to HEVC anchor.