  We consider a parabolic-parabolic interface problem and construct a loosely
coupled prediction-correction scheme based on the Robin-Robin splitting method
analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of
the correction step converge at $\mathcal O((\Delta t)^2)$, under suitable
convergence rate assumptions on the discrete time derivative of the prediction
step, where $\Delta t$ stands for the time-step length. Numerical results are
shown to support our analysis and the assumptions.
