Streaming instability is a powerful mechanism which concentrates dust grains in protoplanetary discs, eventually up to the stage where they collapse gravitationally and form planetesimals. Previous studies inferred that it should be ineffective in viscous discs, too efficient in inviscid discs and may not operate in local pressure maxima where solids accumulate. From a linear analysis of stability, we show that streaming instability behaves differently inside local pressure maxima. Under the action of the strong differential advection imposed by the bump, a novel unstable mode develops and grows even when gas viscosity is large. Hence, pressure bumps are found to be the only places where streaming instability occurs in viscous discs. This offers a promising way to conciliate models of planet formation with recent observations of young discs.