Although development economics has a broad range and captures all of the dimensions of human life, development was often seen in terms of increase in the level of productivity or income. This paper extends the convergence concept to the broader measures of development and standard of living. For this purpose, a development index was constructed as an alternative to Human Development Index of United Nations Development Programme by considering the critiques that were directed to it. Actually, we have two arguments in the approaches proposed as an alternative to the HDI. These are as follows: Calculating HDI without logarithmic transformation of the income dimension. Instead of multiplying the values of health, education and income, collecting the square roots of these three components in order to reach HDI. Two types of convergence (β and σ convergence) test was constructed with the new index and results indicated that there exists less convergence in the development levels of the 76 city in the Turkey for the years 1997-2014 against the results from original HDI which favors more convergence.

Keywords: Human Development Index, Convergence, Development.