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 four 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. Include the gini coefficient in HDI calculations. Taking the arithmetic average of these three components by using the HDI formula in 1994 HDR again. 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 95 countries in the sample for the years 1980-2015 against the results from original HDI which favors more convergence.

Keywords: Human Development Index, Convergence, Education, Health.