A new ordered (Li/Ag)CoO2 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)CoO2 precursor. This compound is actually an intermediate step to the final D4-AgCoO2 delafossite and can be isolated thanks to the kinetics difference between the Li+/Ag+ and Na+/Ag+ exchange processes. It crystallizes in the P6(3)/mmc space group with cell parameters a(hex.) = 2.848(3) angstrom and c(hex.) = 21.607(7) angstrom. The details of the structure as well as its thermal stability and transport properties are presented and discussed.