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We have reduced and analyzed the Infrared Space Observatory (ISO) Short-Wavelength Spectrometer (SWS) spectra of 29 infrared carbon stars with a silicon carbide feature at 11.30 mum, 17 of which have not been previously published. Absorption or emission features of C-2, HCN, C2H2, C-3 and silicon carbide (SiC) have been identified in all 17 unpublished carbon stars. In addition, two unidentified absorption features at 3.50 and 3.65 mum are listed for the first time in this paper. We classify these 29 carbon stars into groups A, B, C and D according to the shapes of their spectral energy distribution, and this classification seems to show an evolutionary sequence of carbon stars with an SiC feature. Moreover we have found the following results for the different groups: on average, the relative integrated flux of the 3.05 mum C2H2+HCN absorption feature increases gradually from group A to B and C; that of the 5.20 mum C-3 absorption feature becomes gradually weaker from group A to B and C; that of the 11.30 mum SiC emission feature increases gradually from group A to B and C but weakens in group D; and in contrast, that of the 13.70 mum C2H2 absorption feature weakens gradually from group A to B and C but becomes stronger in group D. We suggest that the evolution of the IR spectra of carbon stars along the sequence A to D is a result of the following phenomena: as the near-IR black-body temperature (T-nir) decreases, the circumstellar envelope becomes thicker; also the effective temperature (T-eff) of the photosphere of the central star decreases gradually and the C/O ratio increases from A to B.