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During consecutive large picture information changes under limited bandwidth, the use of constant bit rate (CBR) encoding for high definition television (HDTV) broadcasting systems often causes serious picture quality degradation due to the tight constraint on small buffering delay, whereas a variable allocation of bits depending on the picture information changes results in large buffering delay. In this paper, we propose a frame-layer variable bit rate (VBR) video encoding method for maintaining locally consistent picture quality of an encoded video with small buffering delay, which can be used for a video on demand (VOD) system which streams an encoded video file to a client device under limited bandwidth or a real-time streaming application allowing a small delay. An objective function defined as a sum of the local distortion variation of the encoded pictures and the underflow levels at the decoder buffer is minimized with respect to the discrete frame-layer quantization step sizes subject to a constraint on the target number of bits within a temporal sliding window. Then, the constrained discrete minimization problem is converted to an unconstrained continuous minimization problem by introducing a Lagrange multiplier and is solved by applying the first-order necessary condition for local minima with respect to the quantization step sizes. Experimental results demonstrate that the proposed method provides a lower local standard deviation of PSNR comparing with the recent VBR method by 29.2% on average with small buffering delay.