The solar rotation rate at latitudes 0 deg, 15 deg and 30 deg has been inferred by averaging the results of 120 regions of 15 degx15 deg, which have been studied over a total area of about 75 deg in latitude and 360 deg in longitude. A local helioseismology technique, the ring diagram analysis method, has been used to analyse the horizontal velocity vectors from about 0.95 R_solar up to the surface. Our results are in very good agreement with those of other authors over most of the depth range. However, near the surface we find sharp local features which are not reported in other studies. The independent measurements of the rotation rate in the north and south hemispheres show asymmetries below 0.975 R_solar. The data used are full-disc dopplergrams taken by Solar Oscillation Investigation/Michelson Doppler Imager (SOI/MDI) on board of the SOlar and Heliospheric Observatory (SOHO) during its first Dynamic Program, between 1996 May and June.