Since December 2019, the coronavirus disease 2019 (COVID-19) caused by a novel coronavirus SARS-CoV-2 has rapidly spread to almost every nation in the world. Soon after the pandemic was recognized by epidemiologists, a group of biologists comprising the ARTIC Network, has devised a multiplexed polymerase chain reaction (PCR) protocol and primer set for targeted whole-genome amplification of SARS-CoV-2. The ARTIC primer set amplifies 98 amplicons, which are separated only in two PCRs, across a nearly entire viral genome. The original primer set and protocol showed a fairly small amplification bias when clinical samples with relatively high viral loads were used. However, as sample's viral load become low, rapid decrease in abundances of several amplicons were seen. In this report, we will show that dimer formations between some primers are the major cause of coverage bias in the multiplex PCR. Based on this, we propose 12 alternative primers in total in the ARTIC primer set that were predicted to be involved in 14 primer interactions. The resulting primer set, version N1 (NIID-1), exhibits improved overall coverage compared to the ARTIC Network's original (V1) and modified (V3) primer set.