We generalize and prove the recursive relation \[ S_λ(V) = \sum_{L\subseteq V\text{ line}} S_λ(V \mathbin{/\mkern-5mu/} L) \] conjectured by I. G. Macdonald for his "7th variation" of the Schur functions. This variation is a family of polynomials over a finite field that mimic the (straight and skew) Schur polynomials using powers of the Frobenius.