In the past, we always use the realized covariation to estimate the quadratic covariation which plays an important role in many areas of finance. However, we found that when the multiple records appear, the traditional consistent estimator: realized covariation does not work as before. In this thesis, we consider a new estimator of the quadratic covariation concerning two diffusion processes so that this new estimator will still work when we use the non-equally spaced high frequency data with multiple records. We will also establish its consistency and the asymptotic normality in this thesis. Moreover, simulation studies will be given to confirm the finite sample performance of the estimator.