  Using dark matter haloes identified in a large $N$-body simulation, we study
halo assembly bias, with halo formation time, peak maximum circular velocity,
concentration, and spin as the assembly variables. Instead of grouping haloes
at fixed mass into different percentiles of each assembly variable, we present
the joint dependence of halo bias on the {\it values} of halo mass and each
assembly variable. In the plane of halo mass and one assembly variable, the
joint dependence can be largely described as halo bias increasing outward from
a global minimum. We find it unlikely to have a combination of halo variables
to absorb all assembly bias effects. We then present the joint dependence of
halo bias on two assembly variables at fixed halo mass. The gradient of halo
bias does not necessarily follow the correlation direction of the two assembly
variables and it varies with halo mass. Therefore in general for two correlated
assembly variables one cannot be used as a proxy for the other in predicting
halo assembly bias trend. Finally, halo assembly is found to affect the
kinematics of haloes. Low-mass haloes formed earlier can have much higher
pairwise velocity dispersion than those of massive haloes. In general, halo
assembly leads to a correlation between halo bias and halo pairwise velocity
distribution, with more strongly clustered haloes having higher pairwise
velocity and velocity dispersion. However, the correlation is not tight, and
the kinematics of haloes at fixed halo bias still depends on halo mass and
assembly variables.
