first we need to know what kind of bird. Second how long have u had the first bird. Third do they seem healthy "good feathers reg eating ect." forth how close were u and ur bird before u got the new one could u handle it and love it pet it ect..
1. Ur bird may be jelous of the new one and trying to secure its relashionship with u.
2.if there love birds u need to keep the ones with the white rings around there eyes with there own kind and same with the ones without the white ring.
3.sometmes animals just dont get along...
I think that the bird you first had, is jealous of you bringing another one into the home for obvious reasons. I think he's worried that you will pay more attention to ur new bird. He may be wanting to fight to draw attention to his self, its only natural. JUst pay equal amount of time with both of them, but make sure you dont leave him out. I think after a while they may calm down and get used to eachother. In the mean time, i dont know what to suggest, just dont leave them alone that much as the fighting could get out of hand.