Two new members of copper oxybromides M2Cu3O4Br2 (M=Sr,Ba) have been prepared and studied by X-ray powder diffraction. They were determined to assume a tetragonal crystal structure with space group 14/mmm and lattice parameters a=5.4840(2)angstrom, c=13.297(1)angstrom for Sr2Cu3O4Br2 and a=5.5386(2)angstrom, c=14.624(1)angstrom for Ba2Cu3O4Br2. The structure is built of the sheets [Cu3O4] and the fluorite-type layers [M2Br2] stacking alternatively along [001]. The [Cu3O4] layer can be described as the well-known sheets [CuO2] in cuprate superconductors with the addition of Cu to the centers of the square units [CuO2] at a period of square-root 2a(p) x square-root 2a(p). In the alkaline-earth copper oxyhalide systems, M2CuO2X2 can be obtained only with the low ionic radius sum r(M+X) of M2+ and X-, while M2Cu3O4X2 was got only with a high r(M+X) where M=Ca,Sr,Ba and X=Cl,Br.