The invention is directed to a mapping catheter useful for mapping tubular regions in and around the heart. The catheter comprises an elongated tubular catheter body. A mapping assembly is provided at the distal end of the catheter body. The mapping assembly comprises a tubular structure comprising a pre-formed generally circular main region generally transverse and distal to the catheter body and having an outer circumference. The tubular structure comprises a non-conductive cover over at least the main region of the mapping assembly. A plurality of electrodes are carried by the generally circular main region of the mapping assembly. A control handle is mounted at the proximal end of the catheter body. A contraction wire extends through the catheter body and non-conductive cover of the mapping assembly for contracting the generally circular main region of the mapping assembly. The contraction wire has a distal end anchored in the non-conductive cover and a proximal end anchored to a mechanism in the control handle that facilitates longitudinal movement of the contraction wire relative to the catheter body. The portion of the contraction wire extending through the non-conductive cover is positioned on the side of the generally circular main region closer to the center of the generally circular region.