In this note we suggest a new parallelizable mode of operation for message authentication codes (MACs). The new MAC algorithm iterates a pseudo-random function (PRF) FK:{0,1}m → {0,1}n, where K is a key and m,n are positive integers such that m ≥ 2n. The new construction is an improvement over a sequential MAC algorithm presented at FSE2008, solving positively an open problem posed in the paper – the new mode is capable of fully parallel execution while achieving rate-1 efficiency and “full n-bit” security. Interestingly enough, PMAC-like parallel structure, rather than CBC-like serial iteration, has beneficial side effects on security. That is, the new construction is provided with a more straightforward security proof and with an even better (“-free”) security bound than the FSE 2008 construction.