In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using block diagonal row stochastic matrices (as a special case), we define the relation bdr on c 0 , which is said block diagonal majorization. We also obtain some important properties of P bdr , the set of all bounded linear operators T : c 0 → c 0 , which preserve bdr. Further, it is obtained necessary conditions for a bounded linear operator T on c 0 to be a preserver of the block diagonal majorization bdr. Also, the notion of the basic sequences correspond to block diagonal row stochastic matrices with description of some relevant examples will be discussed