A new concept to build shape memory polymers (SMP) combining outstanding fixity and recovery ratios (both above 99% after only one training cycle) typical of chemically crosslinked SMPs with reprocessability restricted to physically crosslinked SMPs is demonstrated by covalently bonding, through thermoreversible Diels-Alder (DA) adducts, star-shaped poly(epsilon-caprolactones) (PCL) end-functionalized by furan and maleimide moieties. A PCL network is easily prepared by melt-blending complementary end-functional star polymers in retro DA regime, then by curing at lower temperature to favour the DA cycloaddition. Such covalent network can be reprocessed when heated again at the retro DA temperature. The resulting SMP shows still excellent shape memory properties attesting for its good recyclability.