Using the neutrix calculus we introduce and analyse a more general product of distributions than in [4]. In particular, we find the "$\alpha$-product" $x^{\lambda\alpha}_{+\circ}x^\mu_-$ for $\lambda+\mu<-1$, $\lambda,\mu,\lambda+\mu\neq-1,-2,\dots$ and $\alpha=-\lambda-\mu-1-[-\lambda-\mu]$.