  In this article, we construct a natural group homomorphism
  $$ \psi: \text{Br}(f)\to H^{1}_{et}(S,
f_{*}\mathcal{O}_{X}^{\times}/\mathcal{O}_{S}^{\times})$$ for a faithful affine
map $f: X \to S$ of noetherian schemes. Here $\text{Br}(f)$ denotes the
relative Brauer group of $f.$ We also discuss the behavior of Brauer groups for
a subintegral map. Furthermore, we prove a relative version of Kummer's exact
sequence.
