Based on the updated UrQMD transport model, the effect of the symmetry potential energy on the two-nucleon HBT correlation is investigated with the help of the coalescence program for constructing clusters, and the CRAB analyzing program of the two-particle HBT correlation. An obvious nonlinear dependence of the neutron-proton (or neutron-neutron) HBT correlation function (Cnp,nn) at small relative momenta on the stiffness factor γ of the symmetry potential energy is found: when γ 0.8, Cnp,nn increases rapidly with increasing γ, while it starts to saturate if γ 0.8. It is also found that both the symmetry potential energy at low densities and the conditions of constructing clusters at the late stage of the whole process influence the two-nucleon HBT correlation with the same power. density dependence of the symmetry energy, sensitive observables, HBT correlation In recent years, the isospin dependent equation of state (EoS) of both infinite and finite nuclear matter has been investigated in a deeper and broader range. Theoretically, a large amount of probes have been brought out to be sensitively affected by the isovector part of the EoS, i.e., the symmetry energy term. Based on different theories, the symmetry energy has been parameterized in different ways (please see refs. [1 − 3] for details). Among these parametrizations, E sym = S 0 u γ is often used (S 0 being the symmetry energy at the normal density, and u = ρ/ρ 0 the reduced density, while γ is the stiffness factor of the density dependence of the symmetry energy). Especially, the density dependence of the symmetry potential energy is paid much more attention since the uncertainty of the symmetry energy mainly comes from this term. Recently, with some comparisons between the results of experimental data and dynamical model IBUU, the uncertainty in the density dependence of the symmetry energy at subnormal densities is reduced into the range of γ ∼ 0.7 − 1.1, depending on the probable medium modifications of the nucleon transport [4,5] . Nevertheless, recently a quite soft symmetry energy (the corresponding γ factor is only about 0.3) was implied experimentally at very low nuclear densities (ρ N is 0.01 − 0.05 times normal density) [6] . Furthermore, in the most recent analyses by Tsang's group [7] , although they found that several different observables can provide consistent constraints on the density dependence of the symmetry energy, the constraints are still