Self-seeding free electron lasers (FELs) are capable of generating fully coherent X-ray pulses. However, the stability of output pulse energy of hard X-ray self-seeding (HXRSS) FEL is poor. This letter reports the seed energy stability investigation of HXRSS FEL. For the purpose of a more stable HXRSS FEL, this work suggests a relatively broad bandwidth ρt of crystal monochromator, a relatively long electron bunch with energy jitter (r.m.s.) down to a quarter of FEL Pierce parameter ρ, and a larger Bragg angle θB to improve the seed energy stability. Moreover, the angle jitter (r.m.s.) between the SASE pulse incident direction and the crystal surface should be less than (ρ tan θB)/2, and the relative time jitter (r.m.s.) between the electron bunch and the seed should be less than half of the seed bump duration Tt.
