  A generalized triangle group is a group that can be presented in the form $G
= < x,y | x^p=y^q=w(x,y)^r=1>$, where $p,q,r\geq 2$ and $w(x,y)$ is a
cyclically reduced word of length at least 2 in the free product $\Z_p*\Z_q=<
x,y | x^p=y^q=1>$. Rosenberger has conjectured that every generalized triangle
group $G$ satisfies the Tits alternative. It is known that the conjecture holds
except possibly when the triple $(p,q,r)$ is one of $(2,3,2),
(2,4,2),(2,5,2),(3,3,2),(3,4,2)$, or $(3,5,2)$. In this paper we show that the
Tits alternative holds in the case $(p,q,r)=(3,4,2)$.
