The aim of this paper is to present a DD (domain decomposition) algorithm almost optimal in the total computational work for a piece wise orthotropic discretizations on a domain composed of rectangles with arbitrary aspect ratios. The two nonzero coefficients in the diagonal matrix of coefficients before products of first order derivatives in the energy integral of the problem are assumed to be arbitrary positive numbers different for each subdomain. The rectangular mesh of the finite element discretization is uniform on each subdomain and otherwise arbitrary. The main problem in designing the algorithm is the interface Schur complement preconditioning, which is closely related to obtaining boundary norms for discrete harmonic functions on the shape irregular domains. The computational cost of the presented Schur complement and DD algorithms is O( N(log N)^{1/2) arithmetic operations, where N is the number of unknowns.