  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 the 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.

Strongly Correlated Electrons