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In this paper, a new fast encoding algorithm based on an efficient motion estimation (ME) process is proposed to accelerate the encoding speed of the scalable video coding standard. Through analysis of the ME process performed in the enhancement layer, we discovered that there are redundant MEs and some MEs can simply be unified at the fully overlapped search range (FOSR). In order to make the unified ME more efficient, we theoretically derive a skip criterion to determine whether the computation of rate-distortion cost can be omitted. In the proposed algorithm, the unnecessary MEs are removed and a unified ME with the skip criterion is applied in the FOSR. Simulation results show that the proposed algorithm achieves computational savings of approximately 46% without coding performance degradation when compared with the original SVC encoder.