  We present a construction for complementary pairs of arrays that exploits a
set of mutually-unbiased bases, and enumerate these arrays as well as the
corresponding set of complementary sequences obtained from the arrays by
projection. We also sketch an algorithm to uniquely generate these sequences.
The pairwise squared inner-product of members of the sequence set is shown to
be $\frac{1}{2}$. Moreover, a subset of the set can be viewed as a codebook
that asymptotically achieves $\sqrt{\frac{3}{2}}$ times the Welch bound.
