This paper studies the problem of \emph{entropy identity testing}: given sample access to a distribution p and a fully described distribution q (both are discrete distributions over the support of size k), and the promise that either p q or H(p) - H(q) \geqslant \varepsilon, where H(\cdot) denotes the Shannon entropy, a tester needs to distinguish between the two cases with high probability. This improves on the sample complexity bound of \tilde{O}(2 {d/2}n 2/\varepsilon 4) from Canonne, Diakonikolas, Kane, and Stewart (2020), which required an additional assumption on the structure of the (unknown) Bayesian network.