We introduce a fully frustrated XY model with nearest neighbor (nn) and next nearest neighbor (nnn) couplings which can be realized in Josephson junction arrays. We study the phase diagram for 0≤ x ≤ 1 (x is the ratio between nnn and nn couplings). When x < 1/√(2) an Ising and a Berezinskii-Kosterlitz-Thouless transitions are present. Both critical temperatures decrease with increasing x. For x > 1/√(2) the array undergoes a sequence of two transitions. On raising the temperature first the two

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... ublattices decouple from each other and then, at higher temperatures, each sublattice becomes disorderd.