  Using a novel analysis technique, the gluon polarisation in the nucleon is
re-evaluated using the longitudinal double-spin asymmetry measured in the cross
section of semi-inclusive single-hadron muoproduction with photon virtuality
$Q^2>1~({\rm GeV}/c)^2$. The data were obtained by the COMPASS experiment at
CERN using a 160 GeV/$c$ polarised muon beam impinging on a polarised $^6$LiD
target. By analysing the full range in hadron transverse momentum $p_{\rm T}$,
the different $p_{\rm T}$-dependences of the underlying processes are separated
using a neural-network approach. In the absence of pQCD calculations at
next-to-leading order in the selected kinematic domain, the gluon polarisation
$\Delta g/g$ is evaluated at leading order in pQCD at a hard scale of $\mu^2=
\langle Q^2 \rangle = 3 ({\rm GeV}/c)^2$. It is determined in three intervals
of the nucleon momentum fraction carried by gluons, $x_{\rm g}$, covering the
range $0.04 \!<\! x_{ \rm g}\! <\! 0.28$~ and does not exhibit a significant
dependence on $x_{\rm g}$. The average over the three intervals, $\langle
\Delta g/g \rangle = 0.113 \pm 0.038_{\rm (stat.)}\pm 0.036_{\rm (syst.)}$ at
$\langle x_{\rm g} \rangle \approx 0.10$, suggests that the gluon polarisation
is positive in the measured $x_{\rm g}$ range.
