  A new alternative volume operator is constructed for loop quantum gravity by
using the so-called cotriad operators as building blocks. It is shown that the
new volume operator shares the same qualitative properties with the standard
volume operator. Moreover, a new alternative inverse volume operator is also
constructed in the light of the construction of the alternative volume
operator, which is possessed of the same qualitative properties as those of the
alternative volume operator. The new inverse volume operator can be employed to
construct the Hamiltonian operator of matter fields, which may lead to an
anomaly-free on-shell quantum constraint algebra without any special
restriction on the regularization procedure for gravity coupled to matter
fields.
