Let $\tilde{f}$, $\tilde{g}$ be ultradistributions in ${\mathcal{Z}}^{\text{'}}$ and let ${\tilde{f}}_{n}=\tilde{f}*{\delta}_{n}$ and ${\tilde{g}}_{n}=\tilde{g}*{\sigma}_{n}$ where $\left\{{\delta}_{n}\right\}$ is a sequence in $\mathcal{Z}$ which converges to the Dirac-delta function $\delta $. Then the neutrix product $\tilde{f}\diamond \tilde{g}$ is defined on the space of ultradistributions ${\mathcal{Z}}^{\text{'}}$ as the neutrix limit of the sequence $\left\{\frac{1}{2}({\tilde{f}}_{n}\tilde{g}+\tilde{f}{\tilde{g}}_{n})\right\}$ provided the limit $\tilde{h}$ exist in the sense that $$\underset{n\to \infty}{\mathrm{N}\text{-}lim}\frac{1}{2}\langle {\tilde{f}}_{n}\tilde{g}+\tilde{f}{\tilde{g}}_{n},\psi \rangle =\langle \tilde{h},\psi \rangle $$
for all $\psi $ in $\mathcal{Z}$. We also prove that the neutrix convolution product $f\u2666\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}*\phantom{\rule{0.166667em}{0ex}}g$ exist in ${\mathcal{D}}^{\text{'}}$, if and only if the neutrix product $\tilde{f}\diamond \tilde{g}$ exist in ${\mathcal{Z}}^{\text{'}}$ and the exchange formula $$F\left(f\u2666\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}*\phantom{\rule{0.166667em}{0ex}}g\right)=\tilde{f}\diamond \tilde{g}$$
is then satisfied.