Many empirical studies show that there are unusual clusters of palindromes, closely spaced direct and inverted repeats around the replication origins of herpesviruses. In this paper, we introduce two new scoring schemes to quantify the spatial abundance of palindromes in a genomic sequence. Based on these scoring schemes, a computational method to predict the locations of replication origins is developed. When our predictions are compared with 39 known or annotated replication origins in 19 herpesviruses, close to 80% of the replication origins are located within 2% of the genome length. A list of predicted locations of replication origins in all the known herpesviruses with complete genome sequences is reported.