  In this paper we associate an invariant to a biquaternion algebra $B$ over a
field $K$ with a subfield $F$ such that $K/F$ is a quadratic separable
extension and $\operatorname{char}(F)=2$. We show that this invariant is
trivial exactly when $B \cong B_0 \otimes K$ for some biquaternion algebra
$B_0$ over $F$. We also study the behavior of this invariant under certain
field extensions and provide several interesting examples.
