  For nonsingular projective 4-folds V of general type with plurigenus
$P_{m_0}(V) \geq 2$ for some positive integer $m_0$, we show that $\varphi_{m}$
is birational onto its image for all integers $m \geq 76m_0+77$ and the
canonical volume Vol(V) has the lower bound $\frac{1}{1680m_0(m_0+1)^3}$. This
improves earlier results of Meng Chen.
