  Let $F(x,y)$ be an irreducible binary form of degree $\geq 3$ with integer
coefficients and with real roots. Let $M$ be an imaginary quadratic field, with
ring of integers $Z_M$. Let $K>0$. We describe an efficient method how to
reduce the resolution of the relative Thue inequalities \[ |F(x,y)|\leq K \;\;
(x,y\in Z_M) \] to the resolution of absolute Thue inequalities of type \[
|F(x,y)|\leq k \;\; (x,y\in Z). \] We illustrate our method with an explicit
example.
