  Surface structure of a restricted ballistic deposition(RBD) model is examined
on a one-dimensional staircase with free boundary conditions. In this model,
particles can be deposited only at the steps of the staircase. We set up
recurrence relations for the surface fluctuation width $W$ using generating
function method. Steady-state solutions are obtained exactly given system size
$L$. In the infinite-size limit, $W$ diverges as $L^\alpha$ with the scaling
exponent $\alpha=\frac{1}{2}$. The dynamic exponent $\beta$ $(W\sim t^\beta)$
is also found to be $\frac{1}{2}$ by solving the recurrence relations
numerically. This model can be viewed as a simple variant of the model which
belongs to the Kardar-Parisi-Zhang (KPZ) universality class $(\alpha_{KPZ}=
\frac{1}{2} , \beta_{KPZ}=\frac{1}{3})$. Comparing its deposition time scale
with that of the single-step model, we argue that $\beta$ must be the same as
$\beta_{KPZ}/(1-\beta_{KPZ})$, which is consistent with our finding.
