  We compute the one-loop \beta-functions describing the renormalisation of the
coupling constant \lambda and the frequency parameter \Omega for the real
four-dimensional duality-covariant noncommutative \phi^4-model, which is
renormalisable to all orders. The contribution from the one-loop four-point
function is reduced by the one-loop wavefunction renormalisation, but the
\beta_\lambda-function remains non-negative. Both \beta_\lambda and
\beta_\Omega vanish at the one-loop level for the duality-invariant model
characterised by \Omega=1. Moreover, \beta_\Omega also vanishes in the limit
\Omega \to 0, which defines the standard noncommutative \phi^4-quantum field
theory. Thus, the limit \Omega \to 0 exists at least at the one-loop level.
