This paper is a sequel of a previous one (Scalar mesons in a chiral quark m
odel with glueball, fur. Phys. J. A 8, 567 (2000)) where an attempt to cons
truct an effective U(3) x U(3)-symmetric meson Lagrangian with a scalar glu
eball was made. The glueball was introduced by using the dilaton model on t
he base of scale invariance. The scale invariance breaking because of curre
nt quark masses and the scale anomaly of QCD reproduced by the dilaton pote
ntial, was taken into account. However, in the previous paper, the scale in
variance breaking because of the terms like h(phi)phi (2)(0) and h(sigma)<(
<sigma>)over bar>(2)(0), where phi (0) and <(<sigma>)over bar>(0) are the p
seudoscalar and scalar isosinglets, was not taken into account. These terms
are produced by the part of the 't Hooft interaction that is connected wit
h gluon anomalies. Allowing for the scale invariance breaking by these term
s has a decisive effect on the quarkonium-glueball mixing and noticeably ch
anges the widths of glueball strong decays. Taking account of this addition
al source of the scale invariance breaking and its implications are the sub
ject of the present work. It is also shown that in the decay of a glueball
into four pions, the channel with two rho -resonances dominates.