  We provide the optimal linear bound for the signature of positive four-braids
in terms of the three-genus of their closures. As a consequence, we improve
previously known linear bounds for the signature in terms of the first Betti
number for all positive braid links. We obtain our results by combining bounds
for positive three-braids with Gordon and Litherland's approach to signature
via unoriented surfaces and their Goeritz forms. Examples of families of
positive four-braids for which the bounds are sharp are provided.
