Several instances of anomalously low values of the B(E2;41+→21+)B(E2;21+→0gs+) ratio (B4/2)<1 have previously been observed in several nuclei among the highly neutron deficient W-Os-Pt isotopes with even numbers of neutrons and protons. The relatively large number of cases suggests a striking new phenomenon that currently has no theoretical explanation. A clue to its origin might be achieved by comparing the B4/2 ratios in even-even nuclei with the corresponding ratios of transition rates in neighboring odd-mass nuclei. However, until now only one case (Os169) has been observed with an unusually low corresponding B4/2 ratio, approximately 1σ below 1. Electromagnetic transition rates between excited states in the extremely neutron deficient nuclide Os167 were measured using 15 single-crystal germanium detectors from the jurogam 3 array coupled to the RITU gas-filled separator. The excited states of interest were populated via the Mo92(Kr78,2pn) fusion-evaporation reaction and studied by selecting the rare reaction channel via recoil-α-decay tagging. The lifetimes of low-lying states were measured using the recoil distance Doppler shift method with the APPA plunger device. From the measured lifetimes in the rotational-like band structure assigned to the νi13/2 yrast intruder configuration, the B(E2;17/2+→13/2+) and B(E2;21/2+→17/2+) values were deduced, resulting in the ratio B(E2;21/2+→17/2+)B(E2;17/2+→13/2+)=0.49(10). The results were compared with previous measurements in the Os isotopic chain and theoretical mean-field calculations, implying that the odd neutron valence particle has limited, if any, influence on the B4/2 values for this particular single-particle configuration.