The patching technique has been used for reducing initial waiting time in VOD services. Traditionally the technique has been applied to fixed segment NVOD scheduling. However, variable segment NVOD scheduling is known to have a better server bandwidth and less initial waiting time. In this paper, we propose a new scheduling algorithm for a true VOD service by incorporating the patching technique into variable segment NVOD scheduling. Our algorithm provides jitter-free playback while minimizing the use of the patching bandwidth. We present the proof of the correctness of our algorithm.