  We show that \[\sum_{\substack{p_n\le x\\
p_{n+1}-p_n\ge\sqrt{p_n}}}(p_{n+1}-p_n)\ll_{\varepsilon} x^{3/5+\varepsilon}\]
for any fixed $\varepsilon>0$. This improves a result of Matom\"{a}ki, in which
the exponent was $2/3$.
