We give a new method for calculation of complex and biHermitian structures on
low dimensional real Lie algebras. In this method by use of non-coordinate
basis, we first transform the Nijenhuis tensor field and biHermitian structure
relations on Lie groups to the tensor relations on their Lie algebras. Then we
use adjoint representation for writing these relations in the matrix form and
by solving these matrix relations and use of automorphism groups of four
dimensional real Lie algebras we obtain and classify all complex and
biHermitian structures on four dimensional real Lie algebras.