  For gapped periodic systems (insulators), it has been established that the
insulator is topologically trivial (i.e., its Chern number is equal to $0$) if
and only if its Fermi projector admits an orthogonal basis with finite second
moment (i.e., all basis elements satisfy $\int |\boldsymbol{x}|^2
|w(\boldsymbol{x})|^2 \,\textrm{d}{\boldsymbol{x}} < \infty$). In this paper,
we extend one direction of this result to non-periodic gapped systems. In
particular, we show that the existence of an orthogonal basis with slightly
more decay ($\int |\boldsymbol{x}|^{2+\epsilon} |w(\boldsymbol{x})|^2
\,\textrm{d}{\boldsymbol{x}} < \infty$ for any $\epsilon > 0$) is a sufficient
condition to conclude that the Chern marker, the natural generalization of the
Chern number, vanishes.
