Step 1: Build the chain from the far end backward. Start with the girl and move up one generation: her uncle's father is her grandfather, call him G.
Step 2: G has a daughter, and since the chain must connect back to the girl's own family, this daughter is the girl's mother, M.
Step 3: The son of M, other than the girl herself, is the girl's brother.
\[\boxed{\text{Brother}}\]