  We give a constructive proof for the existence of an $N$-dimensional Bloch
basis which is both smooth (real analytic) and periodic with respect to its
$d$-dimensional quasi-momenta, when $1\leq d\leq 2$ and $N\geq 1$. The
constructed Bloch basis is conjugation symmetric when the underlying projection
has this symmetry, hence the corresponding exponentially localized composite
Wannier functions are real. In the second part of the paper we show that by
adding a weak, globally bounded but not necessarily constant magnetic field,
the existence of a localized basis is preserved.
