Artificially patterned magnonic crystals serve as a promising candidate for the emerging research fields of magnonics and spintronics. Here, we investigate the spin-wave dispersion in a diatomic nanodot lattice made of Ni80Fe20 nanodots of two different diameters placed in close proximity to form a binary magnonic crystal with a complex double-dot unit cell. The frequency dispersion of SW eigenmodes experimentally measured by the Brillouin light-scattering technique is in good agreement with the numerically calculated band structure derived from the linearized Landau-Lifshitz equation. Due to the change of the nature of interaction among the dots in two mutually perpendicular orientation of the applied bias magnetic field, magnonic band structure, including the slope of the dispersion curves, varies significantly. The anisotropic SW propagation is also studied numerically by local excitation of spin-wave …