  In this Letter, we discuss the effects of $p$-wave attractive interaction in
a spin-$1/2$ Bose gas. With a repulsive $s$-wave background interaction, we
show that for weak $p$-wave attraction, one obtains a standard Bose-Einstein
condensate at zero momentum with spins fully polarized. Upon increasing the
$p$-wave attraction, a fragmented condensate state with singlet pair formation
and $p$-wave correlation emerges. We determine the transition point and
investigate the properties of the fragmented condensate using an ansatz wave
function. We construct the relevant Gross-Pitaevskii equations for the
fragmented condensate and show that the sound velocities are anisotropic and
may vanish in specific directions. Based on the many-body wave function, we
also discuss the low-energy spin excitations of the system.
