This paper presents an algorithm for determining whether two triangles in three dimensions intersect. The general scheme is identical to the one proposed by Möller (1997). The main difference is that our algorithm relies exclusively on the sign of 4 × 4 determinants and does not need any intermediate explicit construc- tions which are the source of numerical errors. Besides the fact that the resulting code is more reliable than existing methods, it is also more efficient. The source code is available online.