In this note we consider a large step modification of the Mizuno-Todd-Ye O (sqrt{n}L) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modified algorithm maintains its O (sqrt{n}L)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate problems. To our knowledge, this is the first construction of a superlinearly convergent algorithm with O (sqrt{n}L)-iteration complexity.