We have succeeded in controlling the ideal characteristics of Carbon Nanotube Field Effect Transistor (CNT FET) which shows 1) the extremely high time stability of FET characteristics, 2) the completely no hysteresis characteristics, and 3) the precise control of the transfer characteristics of p-type and n-type only by changing the electrode metals with the different work functions. It is so far considered that the large time instability and hysteresis characteristics in CNT FET were the attribution of the water and oxygen those adhered the surface of the nanotube. Even if these are completely removed, however, CNT FET still shows the large time instability and hysteresis characteristics. We found out not only the water and oxygen but also the residue of the photo-resist which adhered during the fabrication process of CNT FET is the important origin of those problems. We have established the new fabrication process which could completely remove the residue of the photo resist, and the surface of the nanotube is protected by SiN film after heating the CNT at 700C to prevent the adhesion of the water and oxygen. The electrode metal of Ti with the work function of 4.33eV slightly smaller than that of nanotube of 4.8eV, was used. Though the drain current of CNT FET fabricated by the conventional process shows the large time instability of 20~30%, the drain current of CNT FET by new process shows the fluctuation of ~ 0.1% and improvement of the time fluctuation is more than 100times. The transfer characteristics of n-type CNTFET can be easily obtained only by selecting the electrode metal of Ti with the work functions smaller than the nanotube, when the nanotube is completely pure condition. Because of the pure condition of nanotube, the hysteresis Voltage of the present CNT FET shows almost 0V, which is far smaller value compare to the conventional CNTFET. Thus, we have succeeded in realizing the ideal control of the CNT FET characteristics.