Digital imaging and communications in medicine (DICOM) format is the de facto standard for communications between therapeutic and diagnostic modalities. A plan generated by a treatment planning system (TPS) is often exported in DICOM format. BEAMnrc/DOSXYZnrc is a widely used Monte Carlo (MC) package for modelling the Linac head and simulating dose delivery in radiotherapy. It has its own definition of beam orientation, which is not in compliance with the one defined in the DICOM standard. MC dose calculations using information from TPS generated plans require transformation of beam orientations to the DOSXYZnrc coordinate system (c.s.) and the transformation is non-trivial. There have been two studies on the coordinate transformations. The transformation equation sets derived have been helpful to BEAMnrc/DOSXYZnrc users. However, the transformation equation sets are complex mathematically and not easy to program. In this study, we derive a new set of transformation equations, which are more compact, easily understandable, and easier for computational implementation. The derivation of the polar angle θ and the azimuthal angle φ used by DOSXYZnrc is similar to the existing studies by applying a series of rotations to a vector in DICOM patient c.s. The derivation of the beam rotation ϕ(col) for DOSXYZnrc, however, is different. It is obtained by a direct combination of the actual collimator rotation with the projection of the couch rotation to the collimator rotating plane. Verification of the transformation has been performed using clinical plans. The comparisons between TPS and MC results show very good geometrical agreement for field placements, together with good agreement in dose distributions.