Versatile Video Coding (VVC) is the latest video coding standard, finalized in July 2020. Dependent random access point (DRAP) is supported in HEVC and VVC, through a supplemental enhancement information (SEI) message, for improved coding efficiency in the case of random access. A DRAP picture is an inter-coded picture that can only refer to the most recent intra random access point (IRAP) picture earlier in decoding order. A DRAP picture can be used as a random access point in the bitstream given that the associated IRAP picture is available. Although the DRAP picture increases coding efficiency for random access, the performance is limited since only the associated IRAP picture is allowed to be used as the reference picture for DRAP pictures. In this paper, an extended dependent random access point (EDRAP) picture is proposed to further improve the coding efficiency for random access. Specifically, a particular EDRAP picture only relies on some pictures in a set of pictures consisting of the associated IRAP picture and certain EDRAP pictures between the associated IRAP picture and the particular EDRAP picture in decoding order. EDRAP pictures can be used as random access points as long as the few dependent IRAP or EDRAP pictures are provided. Simulation results demonstrate that the proposed method can achieve 10.2% Bj$\phi$ntegaard-Delta rate saving on average compared to VTM-11.0 under random access configuration. It is noted that the support of EDRAP for VVC, through another SEI message, was adopted by the JVET at its 21st meeting in January 2021.