  Let $G$ be a bipartite graph without loops and multiple edges on $v\ge 4$
vertices, which can be drawn on the plane such that any edge intersects at most
one other edge. We prove that such graph has at most $3v-8$ edges for even
$v\ne 6$ and at most $3v-9$ edges for odd $v$ and $v=6$. For all $v\ge 4$
examples showing that these bounds are tight are constructed.
  In the end of paper we discuss a question about drawings of complete
bipartite graphs on the plane such that any edge intersects at most one other
edge.
  {\sc Keywords:} topological graphs, planar graphs, bipartite graphs.
