The ability to do crack propagation simulations relies on computing accurate stress intensity factors (SIFs) at crack tips. For many years, the standard quarter-point shape functions have been widely used for crack tip elements in finite and boundary element analyses. However, experience has shown that while the quarter-point produces reasonably accurate K I (opening) SIF, it is far less successful in predicting K II (sliding) and K III (twisting). As a result, it is more difficult to accurately predict curved crack growth. In this paper, we present an adjustment to the quarter-point crack tip element and employ this element in symmetric-Galerkin boundary integral fracture analysis. The standard quarter-point element is modified so that the near-tip crack opening displacement (COD) satisfies a known constraint, namely that the term linear in the distance to the tip must vanish. In test cases where the SIFs are known exactly, this modified quarter-point element, in conjunction with the Displacement Correlation Technique (DCT), has produced significantly more accurate results than the standard element.