A technique to improve X-ray stress measurement using Debye-Scherrer rings is reported. In previous work, a Fourier-series-based generalization of the cos alpha method was proposed, which can measure the stress from a Debye-Scherrer ring. That technique and the cos alpha method have difficulties in determining the stress when the grain size of the specimen is relatively large and the Debye-Scherrer ring is grainy. To cope with this problem, in-plane averaging has been used to improve the cos alpha method when measuring coarse-grained specimens. In this study, Fourier series analysis is incorporated with in-plane averaging and it is explained how in-plane averaging improves the stress measurement. Furthermore, the validity of the new technique is demonstrated by measuring the stress of a carbon steel specimen.