  We investigate the conditions at which high-mode magnetohydrodynamic (MHD)
waves propagating in a spinning solar macrospicule can become unstable with
respect to the Kelvin--Helmholtz instability (KHI). We consider the
macrospicule as a weakly twisted cylindrical magnetic flux tube moving along
and rotating around its axis. Our study is based on the dispersion relation (in
complex variables) of MHD waves obtained from the linearized MHD equations of
an incompressible plasma for the macrospicule and cool ($\beta = 0$, rate of
the plasma to the magnetic pressure) plasma for its environment. This
dispersion equation is solved numerically at appropriate input parameters to
find out an instability region or window that accommodates suitable unstable
wavelengths on the order of the macro\-spicule width. It is established that an
$m = 52$ MHD mode propagating in a macro\-spicule with width of $6$~Mm, axial
velocity of $75$~km\,s$^{-1}$, and rotating one of $40$~km\,s$^{-1}$ can become
unstable against the KHI with instability growth times of $2.2$ and $0.57$~min
at $3$ and $5$~Mm unstable wavelengths, respectively. These growth times are
much shorter than the macrospicule lifetime, which lasts about $15$~min. An
increase or decease in the width of the jet would change the KHI growth times,
which remain more or less on the same order when they are evaluated at
wavelengths equal to the width or radius of the macrospicule. It is worth
noting that the excited MHD modes are super-Alfv\'enic waves. A change in the
background magnetic field can lead to another MHD mode number $m$ that ensures
the required instability window.
