A new ordered (Li/Ag)CoOb>2b> layered compound with an unusual oxygen packing combining rock salt and delafossite layers is obtained during the (Li+, Na+)/Ag+ ionic exchange from the OP4-(Li/Na)CoOb>2b> precursor. This compound is actually an intermediate step to the final D4-AgCoOb>2b> delafossite and can be isolated thanks to the kinetics difference between the Li+/Ag+ and Na+/Ag+ exchange processes. It crystallizes in the P6b>3b>/mmc space group with cell parameters ab>hex.b> = 2.848(3) 脜 and cb>hex.b> = 21.607(7) 脜. The details of the structure as well as its thermal stability and transport properties are presented and discussed.