Fin kinematics is the key to thrust generation of oscillatory pectoral fins of manta rays. This could be one of the main reasons that fin designs of robotic manta rays are becoming more complex to simulate the fin kinematics more closely so as to generate high thrusts. However, as the trend suggests, the extent of improvement to thrust generation might not be worth the complexities added to the designs. Out-of-the-box design changes that favour the simplicity and yet improve the fin performance can be a sound replicate for the complicated fin design features. One aspect of manta rays' pectoral fins that influences the fin kinematics is the constraint imposed on the movement of their particularly long root chord that is entirely attached to the body of manta rays. Hypothetically, reducing such a constraint can promote the angle-of-attack during flapping, which can improve thrust generation. This paper aims to study if the simple idea of disengagement of the fin root chord from the body, which is obviously a deviation from the nature, can improve thrust generation. An experiment was conducted on thrust generation of four basic fin designs, where different portions of their chord was disengaged from the body step-by-step. The disengagement occurred for each quarter of the chord, starting from the trailing edge towards the leading edge. It was found that the fins with free root chord (minimal attachment to the body) could generate thrust slightly less than the fully constrained fins (full attachment). In addition, it was shown that thrust generation efficiency kept increasing while disengaging the chord further, and reached the maximum for free root chord. This may show that a powerful and yet more efficient fin can be produced with such a deviation from the nature.