An arrangement in connection with a crosscutting saw of a harvester. Herein, a lattice-like structure composed of strips is provided in a saw casing of the crosscutting saw, the structure being substantially on the same section plane as the rotational movement of a chain of the crosscutting saw. The strips are arranged in the saw casing in such a manner that substantially each movement path tangent generated at a lower edge in a guide bar of the chain or at an outer track on the side of the saw casing in the chain wheel is arranged to encounter a surface in the strip. This provides a structure that enhances a controlled removal of sawdust or other pieces flowing to the saw casing during sawing.