Selection and appointment of best people in any job is an important decision. In this regard, management of the universities is one of the concerning subjects and respectively, head of departments are also important due to their influence on the performance of faculties. In this paper the quality of competency based selection and appointment of head of departments has been studied considering five dimensions of professional knowledge, intellectual and behavioral skills, personality characteristics, attitude, insight and honor of people and the gap between present and desired status has been analyzed according to the viewpoints of faculty members of Yazd University. The data has been collected through literature review, interview and questionnaire. The validity of designed questionnaire has been approved by a group of experts. 175 questionnaires have been distributed among faculty members of 30 departments of Yazd University in 2009, out of which, 122 have been completed and returned. The reliability of questionnaire has been computed using Cronbach's alpha as 0.97. The findings imply that at the current status, the dimensions of "personality characteristics" and "professional knowledge" are of most and least concern, respectively. The findings of calculating weighted negative gap in departments imply that less consideration of personality characteristics is the major reason for selection of incompetent head of departments. By ranking elements of this dimension using TOPSIS technique, it has been found that concentration on factors such as challenging, age, resistance against pressure, freshness and sociality and patience could further improve the current status. Therefore, with a proper planning for quality improvement of the elements of the mentioned dimensions, the probable problems and obstacles towards desirable performance of faculties can be rapidly removed.