The linear smoothing spline estimator is modified to remove boundary bias effects. The resulting estimator can be calculated efficiently using an O(n) algorithm that is developed for the computation of fitted values and associated smoothing parameter selection criteria. The asymptotic properties of the estimator are studied for the case of a uniform design. In this case the mean squared error properties of boundary corrected linear smoothing splines are seen to be asymptotically competitive with those for standard second order kernel smoothers.