Time series data entails considering the linearity or nonlinearity along threshold level before processing it to comprise in a model for policy makers to policy implication. Engle and Siklos (2001) claimed that the EG procedure would be misleading in case if time series possesses possible asymmetric relationship. They recommended a model which includes the asymmetric adjustment to get stationarity of error term. This adjustment process is established by Balke and Fomby (1997) to familiarize Threshold co-integration to combine nonlinearity and co -integration along threshold error correction model. The plenty of past and existing foreign studies showed the evidence of asymmetries between the relationship of unemployment and economic growth and points out that Okun‟s coefficient is asymmetric in upswing and downswing phase of the economy because of labor force participation rate and sectori al growth rates. The objective of this study is to estimate the consistent estimate of threshold level in unemployment rate and output by Tong (1983, 1990) method. Furthermore, test the hypothesis of linear cointegration against threshold cointegration and asymmetric adjustment between unemployment rate and outuput by Balke and Fomby (1997) method for the time period of 1964-2012. A single threshold level is obtained in both unemployment rate and output. Further, the null hypothesis of linear cointegration is rejected against threshold cointegration. It is considered that the results of this study would assist the policy makers in formulating diverse policies related to macroeconomic targets like to stabilize prices, achieving targeted level of economic growth and to redu ce the unemployment level and reduce the forecasting error of unemployment rate and output. Supervisor:- Dr.Hafsa Hina