  A normal field on a spacelike surface in $R^4_1$ is called bi-normal if
$K^{\nu}$, the determinant of Weingarten map associated with $\nu$, is zero. In
this paper we give a relationship between the spacelike pseudo-planar surfaces
and spacelike pseudo-umbilical surfaces, then study the bi-normal fields on
spacelike ruled surfaces and spacelike surfaces of revolution.
