The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields +/- h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature T-c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T-f(h) runs from the upper left corner to the lower right corner, while for T < T-f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T = T-f(h) the magnetization profile in(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w proportional to L, while for T > T-f(h) it scales as w proportional to root L. The distribution P(l) of the interface position l (measured along the z-direction from the corners) decays exponentially for T < T-f(h) from either corner, is essentially flat for T = T-f(h), and is a Gaussian centered at the middle of the diagonal for T > T-f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions. (C) 2007 Elsevier B.V. All rights reserved.