A connector which joins two opposing sections of coil tubing or coil tubing to coil tubing tools so as to enable torque applied from one section to be transmitted to the other section is provided. The connector employs varying width and depth grooves into which portions of the sections of coil tubing are deformed so as to create the torque transmitting connection between the connector and sections of coil tubing. Each of the grooves have a narrow width portion and a wide width portion and corresponding shallow depth and deep depth portion. The narrow width portion of one of the grooves is approximately 180° out of phase from the narrow width portion of the other varying width groove.