  We consider the Clarkson-McLeod solutions of the fourth Painlev\'e equation.
This family of solutions behave like $\kappa
D_{\alpha-\frac{1}{2}}^2(\sqrt{2}x)$ as $x\rightarrow +\infty$, where $\kappa $
is an arbitrary real constant and $D_{\alpha-\frac{1}{2}}(x)$ is the parabolic
cylinder function. Using the Deift-Zhou nonlinear steepest descent method, we
obtain the singular asymptotics of the solutions as $x\to-\infty$ when $\kappa
\left( \kappa -\kappa ^*\right )>0$ for some real constant $\kappa ^*$. The
connection formulas are also explicitly evaluated. This proves and extends
Clarkson and McLeod's conjecture that when the parameter $\kappa >\kappa ^*>0$,
the Clarkson-McLeod solutions have infinitely many simple poles on the negative
real axis.
