It is shown that the number of balanced linear 4-partitions of the $n\times n$-grid $G$ can be expressed by means of the number of minimal central crosses of that grid. This relationship enables an easy derivation of the formulae for the number of balanced linear 4-partitions of $G$, in the form of two sums, which depend on parity of $n$. The corresponding two asymptotic formulae are of the form \[ \frac A{i^2}n^2+O(nog n), \] where $A=2$ for $n$ even and $A=6$ for $n$ odd.