A new algorithm for learning binary codes is presented using randomized initial assignments of bit labels to classes followed by iterative refinement to minimize intraclass Hamming distance. This Randomized Intraclass-Distance Minimizing Binary Codes (RIDMBC) algorithm is introduced in the context of face recognition, an area of biometrics where binary codes have rarely been used (unlike iris recognition). A cross-database experiment is presented training RIDMBC on the Labeled Faces in the Wild (LFW) and testing it on the Point-and-Shoot Challenge (PaSC). The RIDMBC algorithm performs better than both PaSC baselines. RIDMBC is compared with the Predictable Discriminative Binary Codes (DBC) algorithm developed by Rastegari et al. The DBC algorithm has an upper bound on the number of bits in a binary code; RIDMBC does not. RIDMBC outperforms DBC when using the same bit code length as DBC's upper bound and RIDMBC further improves when more bits/features are added.