  In this paper we prove an analogue of the Koml\'os-Major-Tusn\'ady (KMT)
embedding theorem for random walk bridges. The random bridges we consider are
constructed through random walks with i.i.d jumps that are conditioned on the
locations of their endpoints. We prove that such bridges can be strongly
coupled to Brownian bridges of appropriate variance when the jumps are either
continuous or integer valued under some mild technical assumptions on the jump
distributions. Our arguments follow a similar dyadic scheme to KMT's original
proof, but they require more refined estimates and stronger assumptions
necessitated by the endpoint conditioning. In particular, our result does not
follow from the KMT embedding theorem, which we illustrate via a
counterexample.
