The concept of the track length estimator is applied to the uncollided point flux estimator (UCF) leading to a new algorithm of calculating fluxes at a point. It consists essentially of a line integral of the UCF, and although its variance is unbounded, the convergence rate is that of a bounded variance estimator. In certain applications, involving detector points in the vicinity of collimated beam sources, it has a lower variance than the “once-more-collided” point flux estimator, and its application is more straightforward.