This paper introduces a new coordinate system for the Lorenz curve. Particular attention is paid to a special case of wide empirical validity. Four alternative methods have been used to estimate the proposed Lorenz curve from the grouped data. The well known inequality measures are obtained as the function of the estimated parameters of the Lorenz curve. In addition the frequency distribution is derived from the equation of the Lorenz curve. An empirical illustration is presented using the data from the Australian Survey of Consumer Expenditure and Finances 1967-68.