  Mutually unbiased bases are an important tool in many applications of quantum
information theory. We present a new algorithm for finding the mutually
unbiased bases for two-qubit systems. We derive a system of four equations in
the Galois field GF(4) and show that the solutions of this system are
sufficient for obtaining the most general set of mutually unbiased bases.
Further, our algorithm is applied to an example and we show that there are
three possible solutions of the system of four equations, each solution leading
to a different set of mutually unbiased bases.
