By using positive operator-valued measure (POVM) instead of the more commonly used collective unitary operation in the quantum teleportation process, Zhan's scheme (Zhan in Phys. Lett. A 336:317, 2005) is generalized to treat an arbitrary (not a special class of ) unknown two-qubit entangled state. Generally speaking, conditioned on Victor's classical message, Alice can create either a copy or an orthogonal-complement copy of the original state. However, it is shown that Alice's perfect clone can be realized with higher probability or even in a deterministic manner via an appropriate unitary operation provided that the state to be cloned is chosen from six special ensembles.Keywords Quantum cloning · Arbitrary two-qubit entangled state · Two-qubit projective measurement · Positive operator-valued measure · Unitary operationThe principles of quantum mechanics supplied many interesting application in the field of information in the last decade, such as quantum computer [1, 2], quantum cryptography [2-5], quantum teleportation [6], quantum secret sharing (QSS) [7][8][9][10][11][12][13][14], and so on. One of the greatest differences between classical and quantum information is that while classical information can be copied perfectly, quantum cannot. In particular, one can not create a duplicate of an arbitrary qubit without destroying the original one [15]. This follows from the no-cloning theorem of Wootters and Zurek [16] (see also [17,18]). However, quantum cloning or approximate cloning is necessary in some quantum information processes [19]. Hence, in literatures various approximate cloning machines have been proposed [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], which operate either in a deterministic or probabilistic way. Very recently Zhan [35] has proposed two quantum cloning protocols. In his first protocol, two maximally entangled two-qubit states (i.e., Bell states) are taken as quantum channel, and a perfect clone of a special class of unknown two-qubit entangled state (i.e., α|00 + β|11 with |α| 2 + |β| 2 = 1) or implementation of its complement state is realized with assistance offered by the unknown N. Xiao-Fei ( )