  We present results for the interaction of two kaons at maximal isospin. The
calculation is based on $N_f=2+1+1$ flavour gauge configurations generated by
the European Twisted Mass Collaboration with pion masses ranging from about
$230$ to $450\,\textrm{MeV}$ at three values of the lattice spacing. The
elastic scattering length $a_0^{I=1}$ is calculated at several values of the
bare strange and light quark masses. We find $M_K a_0 =
-0.385(16)_{\textrm{stat}} (^{+0}_{-12})_{m_s}(^{+0}_{-5})_{Z_P}(4)_{r_f}$ as
the result of a combined extrapolation to the continuum and to the physical
point, where the first error is statistical, and the three following are
systematical. This translates to $a_0 =
-0.154(6)_{\textrm{stat}}(^{+0}_{-5})_{m_s}
(^{+0}_{-2})_{Z_P}(2)_{r_f}\,\textrm{fm}$.
