We consider the problem of detecting and estimating abrupt changes in the variance of a piecewise stationary Gaussian sequence. Following the usual approach of the change-point analysis we define a contrast function and estimate the change-point as the point of maximum contrast. The consistency of such an estimator can be proven using a functional convergence theorem. A natural application of this method is the detection of change in the Hurst index of a piecewise fractional Brownian motion (fBm). Using the stationarity of increments, we can apply it to this problem. In this talk I will present the construction of the estimator and prove its consistency. A relative statistical test will be also discussed. Finally, I will give numerical results for the case of fractional Brownian motion.