Chatter vibration is a major problem in machining. At present, chatter vibration is avoided by changing the cutting conditions based on the stability limit diagram such that chatter vibration does not occur. However, changing the cutting conditions may reduce the productivity. The stability limit is estimated from the relationship between the dynamic characteristics of the machine tool and the cutting conditions. Therefore, we propose a method for avoiding chatter vibration by changing the machine tool rigidity. The dynamic characteristics of a desktop milling machine tool developed in a previous study can be changed by changing the tensile load of the brace bar attached on the frame. We report the transition of the dynamic characteristics and stability limit diagram with changes in the rigidity of the desktop machine tool, and confirm the presence or absence of chatter vibration through machining tests.