  The double star $S(m_1,m_2)$ is obtained from joining the centres of a star
with $m_1$ leaves and a star with $m_2$ leaves. We give a short proof of a new
upper bound on the two-colour Ramsey number of $S(m_1,m_2)$, for positive
$m_1,m_2$ fulfilling $(\sqrt 5+1)m_2/2 < m_1 < 3m_2$. Our result implies that
for all positive $m$, the Ramsey number of the double star $S(2m,m)$ is at most
$4.275m$.
