The spectral energy distribution(SED)of the γ-ray flare observed in July 1997 in BL Lacertae is re-considered.It is pointed out that the optical observations made by Webb et al.showed the associated optical flare has a hard spectrum(the average spectral index αopt ～ 0.48,Fv ∝ v-α),and the ASCA observations made by Tanihata et al.showed very steep spectra in the soft X-ray band(0.7-1.5 keV)(αx～3-4).We find that the flux densities and spectral indices in both the spectrum emitted by relativistic electrons of a power-law energy distribution with a high energy cutoff,and thus the peak of the SED of the synchrotron radiation(in representation of vFv)is located in the EUV-soft X-ray bands.Therefore,the GeV γ-ray emission observed in the July 1997 outburst may be mainly due to the synchrotron self-Compton(SSC)process,contrasting with the current explanations in terms of external radiation Compton(ERC)process,in which the seed photons are mostly taken to be the UV emission from the clouds of the broad emission line region.We argue that the hard optical spectra observed during the γ-ray outburst may be an important signature for the acceleration of high energy electrons(γe～104)in the γ-ray emitting region.