The solution of a canonical problem regarding the diffraction of a plane electromagnetic wave incident, with an arbitrary angle, upon a strip grating formed by infinitely long thin metallic ribbons is found. The formulation is given for any relation between the width of the ribbons and the width between the ribbons. The exact solution is obtained by using Wiener-Hopf techniques in the case of equal width of the ribbon and the spacing. The numerical values of the transmission and reflection coefficients can be evaluated in a simple manner to any desired accuracy. Plots are given for different angles of incidence in a certain frequency range. The closed form of the TE modes scattering matrix is also given.