  Let $a, b$ be distinct, non-constant polynomials in ${\mathbb F}_2 [z]$. Let
$\xi_{a, b}$ be the power series in ${\mathbb F}_2((z^{-1}))$ whose sequence of
partial quotients is the Thue-Morse sequence over $\{a, b\}$. We establish that
$\xi_{a,b}$ is algebraic of degree $4$.
