  Recently, Cai and Su [Phys. Rev. D {\bf 81}, 103514 (2010)] found that the
sign of interaction $Q$ in the dark sector changed in the approximate redshift
range of $0.45\,\lsim\, z\,\lsim\, 0.9$, by using a model-independent method to
deal with the observational data. In fact, this result raises a remarkable
problem, since most of the familiar interactions cannot change their signs in
the whole cosmic history. Motivated by the work of Cai and Su, we have proposed
a new type of interaction in a previous work [H. Wei, Nucl. Phys. B {\bf 845},
381 (2011)]. The key ingredient is the deceleration parameter $q$ in the
interaction $Q$, and hence the interaction $Q$ can change its sign when our
universe changes from deceleration ($q>0$) to acceleration ($q<0$). In the
present work, we consider the cosmological constraints on this new type of
sign-changeable interactions, by using the latest observational data. We find
that the cosmological constraints on the model parameters are fairly tight. In
particular, the key parameter $\beta$ can be constrained to a narrow range.
