Can I introuce a male finch?

Hi Guys, Here is the thing, I have had 4 finches for a long time, two males and two females they have all lived happily together for almost 2 years. Unfortunatly one male dies a few days ago (im not sure why, he was fine in the morning i got back that night and he looked dreadfull then yeah he only lasted a few more hours.) The four birds had paired off into male and female pairs they had nests and everything. When one dies I cleaned out the cage and put new empty nests in and nesting material on the ground. One male female pair made a new nest and are happy but the female who lost her mate is just bouncing around the cage on her own. Now to the question.....I want to get a new mate for the lonely female, i heard you cant have male finches in together is that true, because my two males got along great I dont want to get a male if it will hurt my other male though. So do I get a male friend or female friend for my lonely finch?