The non-linear microwave surface impedance, Z(s) = R-s + iX(s), of patterned YBCO thin films, was measured using a suspended line resonator in the presence of a perpendicular DC magnetic field, H-DC, of magnitude comparable to that of the microwave field, H-rf. Signature of the virgin state was found to be absent even for relatively low microwave power levels, The microwave loss was initially found to decrease for small applied H-DC before increasing again. Also, non-linearities inherent in the sample were found to be substantially suppressed at low powers at these applied fields, These two features together can lead to significant improvement in device performance.