A system and method for determining the genetic data for one or a small set of cells, or from fragmentary DNA, where a limited quantity of genetic data is available, are disclosed. Genetic data for the target individual is acquired and amplified using known methods, and poorly measured base pairs, missing alleles and missing regions are reconstructed using expected similarities between the target genome and the genome of genetically related subjects. In accordance with one embodiment of the invention, incomplete genetic data is acquired from embryonic cells, fetal cells, or cell-free fetal DNA isolated from the mother's blood, and the incomplete genetic data is reconstructed using the more complete genetic data from a larger sample diploid cells from one or both parents, with or without genetic data from haploid cells from one or both parents, and/or genetic data taken from other related individuals.