  Since there are quantization ambiguities in constructing the Hamiltonian
constraint operator in isotropic loop quantum cosmology, it is crucial to check
whether the key features of loop quantum cosmology are robust against the
ambiguities. In this paper, we quantize the Lorentz term of the gravitational
Hamiltonian constraint in the spatially flat FRW model by two approaches
different from that of the Euclidean term. One of the approaches is very
similar to the treatment of the Lorentz part of Hamiltonian in loop quantum
gravity and hence inherits more features from the full theory. Two symmetric
Hamiltonian constraint operators are constructed respectively in the improved
scheme. Both of them are shown to have the correct classical limit by the
semiclassical analysis. In the loop quantum cosmological model with a massless
scalar field, the effective Hamiltonians and Friedmann equations are derived.
It turns out that the classical big bang is again replaced by a quantum bounce
in both cases. Moreover, there are still great possibilities for the expanding
universe to recollapse due to the quantum gravity effect.
