The layered perovskite structures of NaYTiO4 and homologous acid exchange form were investigated via powder X-ray diffraction and high resolution transmission electron microscopy. The NaYTiO4 layered structure differs from the previous investigation of Blasse et al., by the incorporation of perovskite-like 2 octahedra thick lamellae instead of 1 octahedron thick lamellae and by a stacking of slabs which is primitive instead of I-centered with an (a+b)/2 gliding. The exchange of Na+ cations was performed in an acid medium. This experiment suggests that half of the Y3+ ions occupy the perovskite like cavities whereas the Na+ cations are localized in the interlayer space. Consequently, this structure is probably closer to TlBa2CaCu2O7 family compounds than to A(n+1)B(n)O(3n+1) Ruddlesden-Popper type structure with n=1.