Recently,　Gao　and　Yao　established　the　global　existence　and　temporal　decay　rates　of　solutions　for　a　system　of　compressible　Hall-magnetohydrodynamic　fluids　(Gao　and　Yao　in　Discrete　Contin.　Dyn.　Syst.　36:　3077–3106,　2016).　However,　because　of　the　difficulty　of　derivative　loss　in　the　nonlinear　terms,　Gao　and　Yao　could　not　provide　the　temporal　decay　for　the　highest-order　derivatives　of　classical　solutions.　In　this　paper,　motivated　by　the　decomposition　technique　of　both　low　and　high　frequencies　of　solutions　in　(Wang　and　Wen　in　Sci.　China　Math.　65:　1199–1228　2022),　we　further　derive　the　temporal　decay　for　the　highest-order　derivatives　of　the　strong　solutions.　Moreover,　the　decay　rate　is　optimal,　since　it　agrees　with　the　solutions　of　the　linearized　system.　©　2022,　The　Author(s).