A Boolean function f : 0 1 d 0 1 is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make ( d log d ) queries. This result improves upon the ( d log 2 d ) lower bound for the same class of testers due to Chen et al. (STOC, 2017).