This paper presents results of experimental and theoretical investigations of transverse beam stability at injection to Fermilab Booster and discuses a novel scheme for transition crossing allowing to avoid the longitudinal emittance growth related to the transition. At reduced chromaticity a multibunch high order head-tail mode developes with growth time of 12 turns at fractional part of tune close to zero. An estimate of the growth rate based on known sources of impedance results in significantly smaller value and cannot explain observed instability growth rate.