  We consider a truncation of type IIB supergravity on four-torus where in
addition to the Ramond-Ramond 2-form field, the Ramond-Ramond axion (w) and the
NS-NS 2-form field (B) are also retained. In the (w, B) sector we construct a
linearised perturbation carrying only left moving momentum on two-charge
non-extremal D1-D5 geometries of Jejjala, Madden, Ross and Titchener. The
perturbation is found to be smooth everywhere and normalizable. It is
constructed by matching to leading order solutions of the perturbation
equations in the inner and outer regions of the geometry.
