Consistent hydrological models for multiple time steps are needed to respond to the operational requirement of using a model for different objectives and with varied data sets. In this paper, we propose a rationale for multitime step model development based on the temporal consistency of the fluxes modelled. The new methodology is applied for the temporal downscaling of a lumped rainfall-runoff model (GR4J) from daily to sub-hourly time steps, within a coherent modelling framework. The modelling tests are performed at eight time steps from daily to 6-min, for a set of 240 French catchments, for which 2400 flood events were selected. To identify an improved multi-time step model structure, a two-step approach is followed. First, we propose a model diagnosis to evaluate the internal behaviour of the baseline model across time steps, whereby a significant inconsistency was found in the simulated water fluxes, especially interception. Second, we recommend a prognosis to improve the scale invariance of the modelled water balance by matching the model fluxes across time scales. The new model structure retained for sub-daily time steps is derived from the daily baseline model by refining the representation of the interception process, so that the flux-matching condition is satisfied. A complementary modification of the groundwater exchange function is also resumed following a previous study. The structural changes are motivated by the improvement of model flux consistency across time steps, while also improving model performance. This new dual paradigm for model identification, based on both flux coherence and output accuracy, also results in more robust model parameters across time steps.