The Heliconius butterflies are a widely studied adaptive radiation of 46 species spread across Central and South America, several of which are known to hybridise in the wild. Here, we present a substantially improved assembly of the Heliconius melpomene genome, developed using novel methods that should be applicable to improving other genome assemblies produced using short read sequencing. Firstly, we whole genome sequenced a pedigree to produce a linkage map incorporating 99% of the genome. Secondly, we incorporated haplotype scaffolds extensively to produce a more complete haploid version of the draft genome. Thirdly, we incorporated ~20x coverage of Pacific Biosciences sequencing and scaffolded the haploid genome using an assembly of this long read sequence. These improvements result in a genome of 795 scaffolds, 275 Mb in length, with an L50 of 2.1 Mb, an N50 of 34 and with 99% of the genome placed and 84% anchored on chromosomes. We use the new genome assembly to confirm that the Heliconius genome underwent 10 chromosome fusions since the split with its sister genus Eueides, over a period of about 6 million years.