  The blow up problem of the semilinear scale-invariant damping wave equation
with critical Strauss type exponent is investigated. The life span is shown to
be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for
$0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study
\cite{Tu-Lin} on the sub-Strauss type exponent $p<p_S(n+\mu)$. Our novelty is
to construct the suitable test function from the modified Bessel function. This
approach might be also applied to the other type damping wave equations.
