Let $L(x)$ be a slowly varying function at both zero and infinity. The existence of the non-commutative neutrix convolution product of the distributions $x^\lambda_+L(x)$ and $x^\mu_-$ is proved, where $\lambda$, $\mu$ are real numbers such that $\lambda,\mu\notin -\mathbb N$ and $\lambda+\mu\notin-\mathbb Z$. Some other products of distributions are obtained.