On electron kinetic scales, ions and electrons decouple, velocity shear on inertial length ∼de can trigger electromagnetic (EM) Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in inviscid collisionless plasma with a step-function flow. We show that incompressible plasma, the ideal frozen-in condition E+ve×B/c=0 must be broken for to occur. flow, is re...