Knowledge of the genetic relatedness among individuals is essential in diverse research areas such as behavioural ecology, conservation biology, quantitative genetics and forensics. How to estimate relatedness accurately from genetic marker information has been explored recently by many methodological studies. In this investigation I propose a new likelihood method that uses the genotypes of a triad of individuals in estimating pairwise relatedness (r). The idea is to use a third individual as a control (reference) in estimating the r between two other individuals, thus reducing the chance of genes identical in state being mistakenly inferred as identical by descent. The new method allows for inbreeding and accounts for genotype errors in data. Analyses of both simulated and human microsatellite and SNP datasets show that the quality of r estimates (measured by the root mean squared error, RMSE) is generally improved substantially by the new triadic likelihood method (TL) over the dyadic likelihood method and five moment estimators. Simulations also show that genotyping errors/mutations, when ignored, result in underestimates of r for related dyads, and that incorporating a model of typing errors in the TL method improves r estimates for highly related dyads but impairs those for loosely related or unrelated dyads. The effects of inbreeding were also investigated through simulations. It is concluded that, because most dyads in a natural population are unrelated or only loosely related, the overall performance of the new triadic likelihood method is the best, offering r estimates with a RMSE that is substantially smaller than the five commonly used moment estimators and the dyadic likelihood method.