In 1956, M.P. Schüzenberger proved that cyclic groups are the only groups which can appear as syntactic monoids of finite prefix codes. Later in 1985, P. Udomkavanich gave an algorithm to construct all finite prefix codes whose syntactic monoids are inverse semigroups. It was proved that such a code must be biprefix, so it is called a finite inverse biprefix code. In this thesis, for any given n ≥ 2, a finite inverse biprefix code C whose syntactic monoid M(C*) has exactly n nonzero n-classes is constructed via P. Udomkavanich’s algorithm.