The multi-exponential T2 decay of the MRI signal from cerebral white matter can be separated into short T2 components related to myelin water and long T2 components related to intracellular and extracellular water. In this study, we investigated to what degree the apparent myelin water fraction (MWF) depends on the angle between white matter fibers and the main magnetic field. Maps of the apparent MWF were acquired using multi-echo Carr-Purcell-Meiboom-Gill and gradient-echo spin-echo sequences. The Carr-Purcell-Meiboom-Gill sequence was acquired with a TR of 1073 ms, 1500 ms, and 2000 ms. The fiber orientation was mapped with DTI. By angle-wise pooling the voxels across the brain's white matter, orientation-dependent apparent MWF curves were generated. We found that the apparent MWF varied between 25% and 35% across different fiber orientations. Furthermore, the selection of the TR influences the apparent MWF. White matter fiber orientation induces a strong systematic bias on the estimation of the apparent MWF. This finding has implications for future research and the interpretation of MWI results in previously published studies.