  Let $\lambda$ be the Liouville function, defined as $\lambda(n) :=
(-1)^{\Omega(n)}$ where $\Omega(n)$ is the number of prime factors of $n$ with
multiplicity. In 2021, Helfgott and Radziwi{\l}{\l} proved that $$\sum_{n\leq
x} \frac{1}{n} \lambda(n) \lambda(n+1) \ll \frac{\log x}{(\log \log
x)^{1/2}},$$improving earlier results by Tao and Ter\"av\"ainen. We prove that
$$\sum_{n\leq x} \frac{1}{n} \lambda(n) \lambda(n+1) \ll (\log x)^{1-c}$$for
some absolute constant $c>0$. This appears to be best possible with current
methods.
