This paper presents collaborative decoding (co-decoding), a new method to improve machine translation accuracy by leveraging translation consensus between multiple machine translation decoders. Different from system combination and MBR decoding, which postprocess the n-best lists or word lattice of machine translation decoders, in our method multiple machine translation decoders collaborate by exchanging partial translation results. Using an iterative decoding approach, n-gram agreement statistics between translations of multiple decoders are employed to re-rank both full and partial hypothesis explored in decoding. Experimental results on data sets for NIST Chinese-to-English machine translation task show that the co-decoding method can bring significant improvements to all baseline decoders, and the outputs from co-decoding can be used to further improve the result of system combination.