Recursive Diagonal Torus (RDT) is a class of interconnection network for massively parallel computers with 216 nodes. In this paper, message transfer algorithms on the RDT are proposed and discussed. First, a simple one-to-one message routing algorithm called the vector routing is introduced and its practical extension called the floating vector routing is proposed. In the floating vector routing both the diameter and average distance are improved compared with the fixed vector routing. Next, broadcasting and hypercube emulation algorithm scheme on the RDT are shown. Finally, deadlock-free message routing algorithms on the RDT are discussed. By a simple modification of the e-cube routing and a small numbers of additional virtual channels, both one-to-one message transfer and broadcast can be achieved without deadlock.