  Within the framework on non-extensive thermostatistics we revisit the
recently advanced q-duality concept. We focus our attention here on a modified
q-entropic measure of the spatial inhomogeneity for binary patterns. At a fixed
length-scale this measure exhibits a generalised duality that links appropriate
pairs of q and q' values. The simplest q <-> q' invariant function, without any
free parameters, is deduced here. Within an adequate interval q < qo < q', in
which the function reaches its maximum value at qo, this invariant function
accurately approximates the investigated q-measure, nitidly evidencing the
duality phenomenon. In the close vicinity of qo, the approximate meaningful
relation q + q' = 2qo holds.
