  A finite $CW$-complex $X$ is $C$-trivial if for every complex vector bundle
$\xi$ over $X$, the total Chern class $c(\xi)=1$. In this note we completely
determine when each of the following spaces are $C$-trivial: suspensions of
stunted real projective spaces, suspensions of stunted complex projective
spaces and suspensions of stunted quaternionic projective spaces.
