  We use supershadow methods to derive new expressions for superconformal
blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the
four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1
\mathcal{B}_2^\dagger\rangle$, where $\mathcal{A}_i$ and $\mathcal{B}_i$ are
scalar superconformal primary operators with arbitrary dimension and $R$-charge
and the exchanged operator is neutral under $R$-symmetry. Previously studied
superconformal blocks for chiral operators and conserved currents are special
cases of our general results.
