Let F be the free group generated by the letters a and b. let φ be a homomorphism from P to SL2(￠). Lei χ=Trφ(a), y=Trφ(b), z=Trφ(ab) and let w ε F, then Trφ(w) will be a polynomial of variables x, y. z. The main aim of this note is to determine the leading term of Trφ(w). Let σ be an endomorphlsm of F, then σ witl indite a mapping φσ:(Z[x, y, z])3→(Z[x, y.=1)3 which is called the trace mapping associated with σ. We wig establish the recurrence relations of the reading terms and degrees of the iterations of φσ, Moreover, some typical examples are studied.