The present invention provides detectably labeled RNA and DNA oligonucleotide multimers useful as diagnostic probes in medical, biological and chemical applications. A method for synthesizing DNA and RNA oligonucleotides, oligonucleotide multimers, and analogs, preferably those that are detectably labeled, is also provided. Oligonucleotide synthesis is performed by combining a circular single-stranded oligonucleotide template with an effective polymerase and at least two types of nucleotide triphosphate, without the addition of auxiliary proteins, to yield an oligonucleotide multimer comprising multiple copies of a repeated oligonucleotide sequence.