The intrashell quartet states are obtained by exciting two protons and two neutrons from the highest occupied orbital to the lowest unoccupied orbital of the lowest Hartree-Fock solutions for some even-even (N=Z) nuclei in the ds and fp shells. These intrinsic quartet states are found to be very high in energy. The states with good angular momenta are obtained by diagonalizing the Hamiltonian matrix constructed in the basis of the states projected from the lowest prolate and oblate HF states and the quartet excited intrinsic states with proper care of the non-orthogonality of these states. It was observed that for²⁰Ne both the projection as well as the orthogonalization procedures significantly change the energy separations of the original intrinsic states and the low lying excited states do not have a well-defined quartet structure. The excited states of²⁴Mg and²⁸Si which seem to have dominant quartet structure lie very high up in energy. In contrast to these nuclei, quartet excited states are not likely to provide a reasonable description of the eigenstates of the fp shell nuclei⁴⁴Ti,⁴⁸Cr and⁵²Fe.