The mechanism of achieving unidirectional transmission in the gratings, which only contain isotropic dielectric and metallic layers, is suggested and numerically validated. It is shown that significant transmission in one direction and nearly zero transmission in the opposite direction can be obtained in the same intrinsically isotropic gratings as those studied recently in A. E. Serebryannikov and E. Ozbay, Opt. Express 17, 278 (2009), but at a non-zero angle of incidence. The tilting, non-symmetric features of the grating and the presence of a metallic layer with a small positive real part of the index of refraction are the conditions that are necessary for obtaining the unidirectionality. Single- and multibeam operational regimes are demonstrated. The frequency and angle ranges of the unidirectional transmission can be estimated by using the conventional framework based on isofrequency dispersion contours and construction lines that properly take into account the periodic features of the interfaces, but should then be corrected because of the tunneling arising within the adjacent ranges. After proper optimization, this mechanism is expected to become an alternative to that based on the use of anisotropic materials. © 2009 Optical Society of America.