Abstract. In the field of pattern recognition, the design of an efficient decoding algorithm is critical for statistical machine translation. The most common statistical machine translation decoding algorithms use the concept of partial hypothesis. Typically, a partial hypothesis is composed by a subset of source positions, which indicates the words that have been translated in this hypothesis, and a prefix of the target sentence. Thus, the target sentence is generated from left to right obtaining source words in an arbitrary order. We present a new approach, where the source sentence is translated from left to right and the possible word reordering is performed at the target prefix. We implemented this approach using a multi-stack decoding technique for a phrase-based model, and compared it with both a conventional approach and a monotone approach. Our experiments show how the new approach can significantly reduce the search time without increasing the search errors.