A threaded connection partially in a self-locking arrangement includes a first and a second tubular component provided respectively with male and female threaded zone at their respective ends. Only a portion of a first portion with varying thread width of the male threaded zone cooperates by self-locking tightening with only a portion of the second portion with varying thread width of the female threaded zone when made up one into the other. The connection is able to withstand high torques required for special applications such as drilling with casing or intermediate casing.