Half-metallic nature has been experimentally reported for some Cobalt (Co)-based full Heusler alloys, such as Co2MnSi , Co2(Fe-Mn)Si , Co2Fe(Al-Si) . As has been reported in references [2, 3], it is effective to tune the material composition using a '4th element' for maximizing the spin polarization of the conduction electron. At the same time, such a 4th element sometimes increases the exchange stiffness at the interface, which also increases the magnetoresistance (MR) effect at room temperature . In case of Co2(Fe-Mn)Si, a replacement of Mn to Fe causes increase of the exchange stiffness although the Fermi level approaches to the conduction band edge, which can decrease the spin polarization. To prevent the decrease of the spin polarization, we introduced a 5th element, Al, to the quarterly Heusler alloy Co (Fe-Mn)Si.