  We report the effect of carbon doping in Ti-stabilized nonstoichiometric
molybdenum diboride (Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$B$_{2}$, which exhibits
bulk superconductivity below $T_{\rm c}$ = 7.0 K. It is found that
(Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$(B$_{1-x}$C$_{x}$)$_{2}$ maintains the
AlB$_{2}$-type phase with a uniform elemental distribution for $x$ = 0.12 and
0.16. The substitution of carbon for boron leads to a slight increase in
$a$-axis, a remarkable reduction in $c$-axis, the formation of planar defects
along the (100) crystallographic planes, and a shift of the B 1$s$ peaks
towards higher binding energies. Contrary to
(Mo$_{0.96}$Ti$_{0.04}$)$_{0.8}$B$_{2}$, however, no superconductivity is
observed down to 1.8 K for the C-doped samples, which is ascribed to the
electron filling of boron $\pi$ bands resulting from the carbon doping.
