We investigated the order-to-order transition (OOT) of the polystyrene-block-polyisoprene-block-polystyrene-block-polyisoprene (S1I1S2I2) linear tetrablock copolymer at the symmetric volume fraction of total PS and PI blocks but asymmetry of the PI block (tau(PI) = f(PI1)/(f(PI1) + f(PI2)) = 0.19), in which f(PI1) and f(PI2) are the volume fractions of PI in the second and fourth blocks, respectively. Very interestingly, this block copolymer showed cylindrical to lamellar microdomain transition upon heating. Such a behavior is exactly the opposite of commonly observed OOT for the linear AB diblock and A(1)BA(2) triblock copolymers with upper critical ordering transition, where lamellar microdomains have been transformed to cylindrical microdomains upon heating. This interesting transition sequence is due to the chain architecture of the linear tetrablock copolymer with two PS and two PI blocks. Experimentally observed microdomains during the transition are consistent with predicted equilibrium microdomains by the self-consistent field theory.