This paper establishes a protocol for the teleportation of an arbitrary unknown f-dimensional multi-particle entangled state using high-dimensional two-particle entangled channels. We first construct a set of completely orthogonal non-symmetric bases to enable a deterministic teleportation scheme for an f-dimensional two-particle state via two d-dimensional maximally entangled two-qudit states ( \(d>f\) ). Within this framework, the sender executes non-symmetric basis measurements on their particles, and the receiver applies specific unitary operations, contingent upon the measurement outcomes, to faithfully reconstruct the original state. We then extend this protocol to accommodate non-maximally entangled channels, demonstrating that the arbitrary two-particle state can be probabilistically recovered through the introduction of auxiliary qubits and suitable local operations, with the corresponding success probability provided. Analysis confirms that the non-maximally entangled scheme generalizes its deterministic counterpart. Finally, both schemes are directly scalable to teleport an arbitrary unknown f-dimensional k-particle entangled state utilizing k d-dimensional two-qudit channels.
