The transition from inanimate materials to the earliest forms of life must have involved multiplication of a catalytically active polymer that is able to replicate. The semiconservative replication that is characteristic of genetic information transfer requires strands that contain more than one type of nucleobase. Short strands of RNA can act as catalysts, but attempts to induce efficient self-copying of mixed sequences (containing four different nucleobases) have been unsuccessful with ribonucleotides. Here we show that inhibition by spent monomers, formed by the hydrolysis of the activated nucleotides, is the cause for incomplete extension of growing daughter strands on RNA templates. Immobilization of strands and periodic displacement of the solution containing the activated monomers overcome this inhibition. Any of the four nucleobases (A/C/G/U) is successfully copied in the absence of enzymes. We conclude therefore that in a prebiotic world, oligoribonucleotides may have formed and undergone self-copying on surfaces.