This work is to study an order D(P) on maximal antichains of a given order. D(P) is an order included in the order which defines the Lattice of maximal antichains AM(P), introduced by R.P. Dilworth, in 1960. In [3], T.Y. Kong and P. Ribenboim have proved that there exists an integer i such that Di(P) is a chain, where Di(P)=D(D(…D(P))), i times. We find the smallest i, noted cdev(P) such that Di(P) is a chain for some particular classes of orders and we approximate this parameter in the general case of order.