Disclosed herein is a system and method for increasing the fidelity of measured genetic data, for making allele calls, and for determining the state of aneuploidy, in one or a small set of cells, or from fragmentary DNA, where a limited quantity of genetic data is available. Poorly or incorrectly measured base pairs, missing alleles and missing regions are reconstructed using expected similarities between the target genome and the genome of genetically related individuals. In accordance with one embodiment, incomplete genetic data from an embryonic cell are reconstructed at a plurality of loci using the more complete genetic data from a larger sample of diploid cells from one or both parents, with or without haploid genetic data from one or both parents. In another embodiment, the chromosome copy number can be determined from the measured genetic data, with or without genetic information from one or both parents.