First you need to make sure the bird is healthy (as the first answerer suggested)..Once you are positive that the bird is healthy, you need to allow both birds free flight time outside the cage in a small room or somewhere where they won't get hurt or in trouble. Observe their behavior outside the cage, If you allow your bonded bird a lot of free time outside the cage, he may have established some "territories around the house. So if the new bird intrudes on his territory they may fight, so watch for that while they are out of the cage..Budgies are flock animals but they are also very territorial toward newcomers (the new bird), Also bird that are already established and bonded to their owners tend to get jealous of new birds who get a lot of attention.
I would suggest getting a whole new cage for them. This would be neutral territory for each bird until they accept each other as part of their flock. Also you may need two food/water bowls because you want to try and avoid all fights (which is impossible because they will inevitably fight sooner or later to est. a pecking order). watch their behavior in the new cage. are they avoiding each other at all costs? are they staring each other down? if not they should be ok. Lastly to avoid your bird getting jealous you may want to let your bird be the first to do everything (i.e. first to be taken out of the cage, get treats, get attention) but still allow them equal time with you to bond.