  In this paper, we study the Painlev\'{e} VI equation with parameter $(\frac
{9}{8},\frac{-1}{8},\frac{1}{8},\frac{3}{8})$. We prove
  (i) An explicit formula to count the number of poles of an algebraic solution
with the monodromy group $D_{N}$, where $D_{N}$ is the dihedral group of order
$2N$.
  (ii) There are only four solutions without poles in $\mathbb{C}\backslash
\left \{ 0,1\right \} $.
  (iii) If the monodromy group of the associated linear ODE of a solution
$\lambda \left( t\right) $ is unitary, then $\lambda ( t) $ has no poles in
$\mathbb{R}% \backslash \{ 0,1\} $.
