We measured the transverse magnetoresistivity of the mixed valence compound $alpha$-YbAlB$_4$. Two configurations were used where current was applied along [110] direction for both and magnetic field was applied along [-110] and $c$-axis. We found th
e transverse magnetoresistivity is highly anisotropic. In the weak field below 1 T, it is consistent with stronger $c$-$f$ hybridization in the $ab$ plane which was suggested from the previous zero field resistivity measurements. At the higher field above 3 T, we observed a negative transverse magnetoresistivity for the field applied along the $c$-axis. The temperature dependences of the resistivity measured at several different fields suggest the suppression of the heavy fermion behavior at the characteristic field of $sim 5.5$ T.
