We perform systematic investigation of a new method for generating high-order harmonics, using ablation as the nonlinear medium. We place emphasis on clarifying the pump laser conditions for optimum harmonic yield. For this purpose, we use the Ti:Sapphire laser beams of the advanced laser light source (800 nm wavelength, 360 mJ total energy). We have independently varied the intensity of the prepulse (which creates the plasma ablation) and the intensity of the main pulse (which generates the harmonics), and studied their influence on the harmonic intensity. We show here that the presence of doubly ionized atoms in the ablation, created either by a strong prepulse intensity or by irradiating the main pulse, will suppress harmonic generation.