A new first-order phase transition is proposed to manifest itself in rotating 3He-B for the vortex-free state, owing to counterflow. The 'flare-out' texture is found to become spontaneously unstable towards a new 'flare-in' texture, which is suggested to explain the transition, first observedwith theuseofNMRby HakonenandNummilain 1987andconfirmed by Korhonen and co-workers in 1989, to a previously unidentified state characterised by a signalcorrespondingtop = 90",i.e.,withavectorriperpendiculartoH 11 Cl llz. Thistransition is also expected to be observable in other experiments, such as ones based on ultrasonic measurements, on the vortex-free state of rotating superfluid 3He-B, a new tenfold splitting of the real squashing mode is predicted to occur for the flare-in texture.