  We report a high precision search for orbital-like magnetic order in the
pseudogap region of La2-xSrxCuO4 single crystals using zero-field muon spin
relaxation (ZF-muSR). In contrast to previous studies of this kind, the effects
of the dipolar and quadrupolar interactions of the muon with nearby nuclei are
calculated. ZF-muSR spectra with a high number of counts were also recorded to
determine whether a magnetically ordered phase exists in dilute regions of the
sample. Despite these efforts, we find no evidence for static magnetic order of
any kind in the pseudogap region above the hole-doping concentration p = 0.13.
