Direct nitrolysis of 3,7-dinitro-1,3,5,7-tetraazabicyclo[3,3,1]nonane (DPT) is a feasible way to synthesize HMX, and it has multiple practical applications. In this paper, a new nitrolysis process involving the use of an $N_2O_5-HNO_3$ system catalyzed by acidic ionic liquids (AILs) was developed. The results show that [$Et_3NH$]TsO was the best catalyst among the 28 AILs used and that HMX was formed at a higher yield of 61%, compared to 45% without any AIL. Moreover, with the addition of $N_2O_5$, the yield was further increased to a maximum value of 69%. The AILs were also efficiently recovered by simple extractions without any apparent loss of catalytic activity, even after five runs.