Relative Milnor $K$-groups of split nilpotent extensions

Consider the split nilpotent extension $R=S+J$ of a commutative ring $S$, containing $1/2$ and with sufficiently many invertible elements (the degree of nilpotency is 2). We will prove, that the relative Milnor $K$-group $K_2^M(R,J)$ is isomorphic to the quotient 4Omega^1_{R,J}/dJ$ of relative Kaehler differentials by it's $Z$-submodule $dJ$. This can be deduced in a slightly different form from previous results of Van~der~Kallen and S.~Bloch, but in our case the proof will not require any machinery of algebraic $K$-theory and will be given in terms of symbols only.