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Let $R$ be a commutative ring and $I\subset R$ be a nilpotent ideal such thatthe quotient $R/I$ splits out of $R$ as a ring. Let $N$ be a natural numbersuch that ${I^N=0}$. We establish a canonical isomorphism between the relativeMilnor $K$-group $K^{M}_{n+1}(R,I)$ and the quotient of the relative module ofdifferential forms $\Omega^n_{R,I}/d\,\Omega^{n-1}_{R,I}$ assuming that $N!$ isinvertible in $R$ and that the ring $R$ is weakly $5$-fold stable. The lattermeans that any $4$-tuple of elements in $R$ can be shifted by an invertibleelement to become a $4$-tuple of invertible elements.

Relative Milnor $K$-groups and differential forms of split nilpotent extensions