Abstract: A surgical fastening clip of a shape memory alloy which applies a first clamping force to a site when the alloy is in its martensitic condition and a second clamping force to the site when the alloy heats due to surrounding tissue such that the alloy transforms to its austenitic condition. The second clamping force is greater than the first clamping force and prevents the clip from slipping or falling off the clamped site due to shrinkage or movement of the site. For instance, the site could be a blood vessel which becomes thinner due to the compressive force of the clip and shrinks, but the clip maintains a clamping force on the blood vessel due to the shape memory effect of the alloy. A method of using a surgical fastening clip formed of a shape memory alloy by placing opposed legs of the clip around a site, deforming the legs to a closed configuration and heating the clip by the natural surroundings to cause further closing of the legs and thereby increasing the clamping force.