Soft catheter for linear mapping stabilizing tip

A mapping catheter adapted for mapping near a tubular region of a heart, comprising: a body of elongated tubular catheter having an outer wall, a proximal end and a distal end, and at least one lumen extending through the same; an intermediate section (14) having a proximal end and a distal end, with the distal intermediate section of the catheter body; and mounting mapping at the distal end of the intermediate section assembly having mapping: a main segment generally circular (46) with a support member having shape-memory disposed within at least the main segment assembly mapping a proximal generally linear segment (38) to the main segment generally circular, having generally linear segment greater flexibility than the intermediate section and the main segment generally circular, and a plurality of ring electrodes in the generally linear segment, where the main segment generally circular is adapted to releasably securable itself in the tubular region and wherein the generally linear segment is adapted to generally contact along its length with the tissue of the heart wall near an ostium of the tubular region.