A polymer, which by pyrolysis transforms into Al–C–N–(O) ceramics, was synthesized from trimethylamine alane and cyan amide, and its applicability as a sintering additive for Si3N4 was investigated. Si3N4 powders were mixed with the precursor by treatment with organic slurries of the precursor to induce the homogeneous distribution of the additive. The green-bodies were pretreated in air or NH3 at 800 °C to control the chemical composition of the additive, through which the densification of Si3N4 could be improved. Dense samples with very fine grains (<2 μm) were obtained after sintering at 1600 °C in 0.1 MPa N2. Besides silicon nitride, submicrometer silicon carbide particles were observed in the samples, indicating that this procedure (i.e., the use of this novel sintering additive) also allows for the fabrication of SiC–Si3N4 composites.