  We give an adaptive algorithm which tests whether an unknown Boolean function
$f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either
non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided
error using $\widetilde{O}(n^{3/4}/\epsilon^2)$ queries. This improves on the
best adaptive $O(n/\epsilon)$-query algorithm from Baleshzar, Chakrabarty,
Pallavoor, Raskhodnikova and Seshadhri when $1/\epsilon \ll n^{1/4}$. Combined
with the $\widetilde{\Omega}(n)$-query lower bound for non-adaptive algorithms
with one-sided error of [CWX17, BCPRS17], we conclude that adaptivity helps for
the testing of unateness with one-sided error. A crucial component of our
algorithm is a new subroutine for finding bi-chromatic edges in the Boolean
hypercube called adaptive edge search.
