  Near the point of tangent bifurcation, the scaling properties of the laminar
length of type-I intermittency are investigated in the presence of noise. Based
on analytic and numerical studies, we show that the scaling relation of the
laminar length is dramatically deformed from $\frac{1}{\sqrt{\epsilon}}$ for
$\epsilon >0$ to $\exp\{\frac{1}{D}|\epsilon|^{3/2}\}$ for $\epsilon<0$ as
$\epsilon$ passes the bifurcation point $(\epsilon=0)$. The results explain why
two coupled R\"ossler oscillators exhibit deformation of the scaling relation
of the synchronous length in the nearly synchronous regime.
