We consider the 2D J_1-J_2 classical XY model on a square lattice. In the frustrated phase corresponding to J_2>J_1/2, an Ising like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete Z_2 symmetry plus the U(1) global one. Using a powerful algorithm we show that the system undergoes two transitions at different but still very close temperatures, one of Kosterlitz-Thouless (KT) type and another one which does not belong to the expected Ising universality class. A new analysis of the KT transition has been developed in order to avoid the use of the non-universal helicity jump and to allow the computation of the exponents without a precise determination of the critical temperature. Moreover, our huge number of data enables us to exhibit the existence of large finite size effects explaining the dispersed results found in the literature concerning the more studied frustrated 2D, XY models.[ postscript.gz]

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