A new polytype of AgCoO2 delafossite has been prepared from the ordered OP4-(Li/Na)CoO2 layered compound using ion-exchange reaction in molten salts, As expected from the structural model assuming a topotactic process, the lamellar structure of this new polytype is an alternate combination of the already known 2H and 3R delafossite polytypes. It crystallizes in the P6(3)/mmc space group with cell parameters a(hex.) = 2.871(1) angstrom and c(hex.) = 24.448(1) angstrom. Thermal stability, morphology characterization, and electrical properties are reported here and compared with those of the 2H and 3R AgCoO2 polytypes.