An exact solution of the scattering problem in 2D square-corner discontinuities is presented in an explicit form. This suggests an efficient computational procedure for characteristics of electron ballistic transport in square-corner shaped waveguides. Using the proposed method, bound-state energies, mode-to-mode as well as total and averaged transmission probabilities, in a square-corner right-angle bend have been calculated. Conductance and electron-filtering properties of the system are found to be challenging problems for its practical realization.