Let \(\Gamma\) be a group, \(K\) a \(\Gamma\)-field, i.e., a field on which \(\Gamma\) acts by automorphisms, and \(H^2(\Gamma;K^*)\) the second cohomology group of \(\Gamma\) with coefficients in the multiplicative group \(K^*\) of \(K\) (viewed as a \(\Gamma\)-module). By definition, the equivariant Brauer group \(\text{Br}(K,\Gamma)\) of Fröhlich-Wall consists of equivalent Morita-equivalence classes of central simple \((K,\Gamma)\)-algebras, i.e., of central simple \(K\)-algebras endowed with a \(\Gamma\)-action by ring automorphisms extending the given \(\Gamma\)-action on \(K\). For any extension \(E/K\) of \(\Gamma\)-fields, the relative equivariant Brauer group \(\text{Br}(E/K,\Gamma)\) is the kernel of the induced homomorphism of \(\text{Br}(K,\Gamma)\) into \(\text{Br}(E,\Gamma)\). The paper under review shows that if \(E/K\) is a finite Galois extension with Galois group \(G\), then there is a natural exact sequence \[ 0\to\text{Br}(E/K,\Gamma)\to H^2(G\times\Gamma;E^*)\to H^2(\Gamma;E^*), \] where \(G\times\Gamma\) is the semidirect product group associated with the diagonal \(\Gamma\)-action on \(G\). When \(\Gamma=1\), this is equivalent to the classical description of the relative Brauer group \(\text{Br}(E/K)\) in terms of similarity classes of crossed products and its interpretation in the language of Galois cohomology. The main result is obtained in a more explicit form in Section 3 of the paper, which is used for deriving two interesting consequences (as the authors point out, one of these is due to the reviewer).