Small-angle neutron scattering (SANS) is measured on a lamellar phase in C16E7 (hepta(oxyethylene glycol)-n-hexadecylether) /water system (40 - 55 wt% of C16E7) at 70 °C under shear flow. As the shear rate increases from 0.3 to 1 s-1, the repeat distance (d) is reduced suddenly and discontinuously. With the further increase in the shear rate, d increases slightly after taking a minimum (d∗). These results are obtained for all the principal orientations of lamellae. While d at rest increases from 6.5 nm to 8.5 nm with decreasing concentration from 55 to 40 wt%, d∗ is almost independent of concentration and nearly equal to the thickness of bilayers (∼ 5 nm) obtained from the line shape analysis of small angle X-ray scattering at rest. These results suggest segregation into surfactant-rich and water-rich regions.