  In this paper, we first prove that $u,v,h$ are linearly dependent over ${\bf
K}$ if $JH$ is nilpotent and $H$ has the form: $H=(u(x,y,z),v(u,h),h(x,y))$
with $H(0)=0$ or $H=(u(x,y),v(u,h),h(x,y,z))$ with $H(0)=0$. Then we classify
polynomial maps of the form $H=(u(x,y),v(x,y,z), h(x,y))$ in the case that $JH$
is nilpotent and $(\deg_yu,\deg_yh)\leq 2$.
