I consider a bivariate stationary fractional cointegration system and I propose a quasi-maximum likelihood estimator based on the Whittle analysis of the joint spectral density of the regressor and errors to estimate jointly all parameters of interest of the model: the long run coefficient and the long memory parameters of the regressor and errors. I lead a Monte Carlo experiment which reveals the good finite sample properties of this estimator, even when the parameter space is extended to the non-stationary regions. An application to the stock market synchronization is proposed to illustrate the empirical relevance of this estimator.