The plasma Raman instability can efficiently compress a nanosecond long high-power laser pulse to sub-picosecond duration. Although, many authors envisaged a converging beam geometry for Raman amplification, here we propose the exact opposite geometry; the amplification should start at the intense focus of the seed. We generalise the coupled laser envelope equations to include this non-collimated case. The new geometry completely eradicates the usual trailing secondary peaks of the output pulse, which typically lower the efficiency by half. It also reduces, by orders of magnitude, the initial seed pulse energy required for efficient operation. As in the collimated case, the evolution is self similar, although the temporal pulse envelope is different. A two-dimensional particle-in-cell simulation demonstrates efficient amplification of a diverging seed with only 0.3 mJ energy. The pulse has no secondary peaks and almost constant intensity as it amplifies and diverges.