The present invention relates to a method for generating transcripts from: at least one RNA sequence to be amplified comprising a "primer" region and a region of interest, and an amplification primer comprising a promoter region, and a region capable of hybridizing to said "primer" region of the RNA sequence to be amplified, said method being carried out at constant temperature, and comprising the following steps: a) said primer is hybridized with the RNA to be amplified, b) the primer is extended by means of a reverse transcriptase enzymatic activity in order to generate a complementary deoxyribonucleic acid (cDNA) sequence of the RNA to be amplified, c) the RNA to be amplified, hybridized to said cDNA, is cleaved by means of an enzyme that has a ribonuclease H activity, so as to obtain fragments of RNA to be amplified, hybridized to said cDNA, d) the ends of said fragments of RNA to be amplified are extended by means of a reverse transcriptase and strand displacement enzyme, so as to obtain RNA-DNA/DNA hybrids, e) RNA transcripts are obtained from the RNA-DNA/DNA hybrids formed in step d), by means of an enzyme that has an RNA polymerase activity.