  An embedding of a graph in $3$-space is linkless if for every two disjoint
cycles there exists an embedded ball that contains one of the cycles and is
disjoint from the other. We prove that every bipartite linklessly embeddable
(simple) graph on $n\ge5$ vertices has at most $3n-10$ edges, unless it is
isomorphic to the complete bipartite graph $K_{3,n-3}$.
