We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preserves near horizon fall-off conditions. Subsequently, we find supertranslation, superrotation and multiple-charge modes. We apply the obtained results on a typical static dilaton black hole and on a charged rotating black string, as examples. In this case, supertranslation doublezero-mode charge T (0,0) is not equal to black hole entropy times Hawking temperature. This may be seen as a problem but it is not, because, in Einstein-Maxwell-Dilaton theory, we have a U(1) gauge freedom and we use an appropriate gauge fixing to fix that problem. We show that new entropy formula 4πĴ + 0Ĵ − 0 , proposed in [5], is valid for black strings as well as black holes. * Electronic address: rezakord@ipm.ir † Electronic address: hamed.adami@yahoo.com