The local magnetic field in the bulk of superconducting single crystal  tin was measured near and across the transition between the normal ͑N͒ and intermediate ͑I͒ state at Tϭ0.08 K. With varying applied field H a , the data indicate a reversible phase transition within the I state at H t Ϸ295 Oe, interpreted as a transition from the laminar to a tubular structure. Near the I→N transition, occurring at H cI ϭ0.98H c0 ϭ300 Oe, the field B in the N domains is strongly inhomogeneous with B ϽH c0 , it grows with the decrease of H a towards the value H c0 ϭ305.5Ϯ0.5 Oe. On lowering H a in the N state, a large ''field supercooling'' (␦H/H c Ϸ6%) of this state was observed.