The crew of a Saab 340 aircraft reported downwind at Ballina NSW for runway 24, in marginal VMC with passing showers. A Mitsubishi MU2 aircraft was also operating within the MBZ and the two aircraft had established two way communications. The Saab crew reported that they were established on final approach for runway 24 when the MU2 turned for a tight base leg in front of them. The crew of the Saab broadcast their position on short final for runway 24. Although they state the pilot of the MU2 did not respond to this call, he flew through the centre line of the runway and continued north with his landing gear extended. The pilot of the MU-2 stated to the owner of the aircraft, that he had broadcast his position joining downwind. As he received no reply to this call, he assumed that the Saab had already landed and continued the approach. He also made a broadcast turning base, and received a reply from the Saab that they were established on final. Due to other traffic in the area he completed a holding pattern before attempting another approach.