Previously unknown isotopes (30)Ar and (29)Cl have been identified by measurement of the trajectories of their in-flight decay products (28)S+p+p and (28)S+p, respectively. The analysis of angular correlations of the fragments provided information on decay energies and the structure of the parent states. The ground states of (30)Ar and (29)Cl were found at 2.25(-0.10)(+0.15) and 1.8±0.1 MeV above the two- and one-proton thresholds, respectively. The lowest states in (30)Ar and (29)Cl point to a violation of isobaric symmetry in the structure of these unbound nuclei. The two-proton decay has been identified in a transition region between simultaneous two-proton and sequential proton emissions from the (30)Ar ground state, which is characterized by an interplay of three-body and two-body decay mechanisms. The first hint of a fine structure of the two-proton decay of (30)Ar*(2(+)) has been obtained by detecting two decay branches into the ground and first-excited states of the (28)S fragment.