The popular Adjusted Rand Index (ARI) is extended to the task of simultaneous clustering of the rows and columns of a given matrix. This new index called Coclustering Adjusted Rand Index (CARI) remains convenient and competitive facing other indices. Indeed, partitions with high numbers of clusters can be considered and it does not require any convention when the numbers of clusters in partitions are different. Experiments on simulated partitions are presented and the performance of this index to measure the agreement between two pairs of partitions is assessed. Comparison with other indices is discussed.