Plane wave reflection from a planar rectangular array of C-shaped wire elements placed over or on a (metal-backed) Dallenbach absorbing layer is considered. An explicit method is introduced after approximating each C-particle as a pair of electric and magnetic dipoles. Unlike our previous method, the present explicit method is valid even when the wire elements are near or on the dielectric-air interface of the Dallenbach absorbing layer. Such an explicit method is very useful for optimal design of thin and low profile anti-reflection structure involving array of C-shaped wire elements. Numerical results are presented to illustrate the anti-reflection effect, in particular, when the C-shaped wire elements touch the dielectric-air interface of the Dallenbach absorbing layer.