Inhibits signal transduction by increasing the GTPase activity of G protein alpha subunits thereby driving them into their inactive GDP-bound form. Activity on G(z)-alpha is inhibited by phosphorylation of the G protein. Activity on G(z)-alpha and G(i)- alpha-1 is inhibited by palmitoylation of the G protein. This is the function of RGS4 (regulator of G protein signaling 4, ENSG00000117152).