Testing zero variance component in linear mixed models can be performed using an exact F-test. The test statistic is derived using a decomposition that is valid regardless of the unknown covariance structure of the random effects. The  decomposition splits the log-likelihood function into two functions that repersent the between and within cluster variability in a traditional analysis  of variance problem. Results from numerical simulatin studies reveal that F-test has a competing power compared to distribution free permutation tests. An application to real set is provided.