Recently, Bich et al. (Int. J. Theor. Phys. 51: 2272, 2012) proposed two deterministic joint remote state preparation (JRSP) protocols of an arbitrary single-qubit state: one is for two preparers to remotely prepare for a receiver by using two Einstein-Podolsky-Rosen (ERP) pairs; the other is its generalized form in the case of arbitrary N (N > 2) preparers via N ERP pairs. While examining these two protocols, we find that the success probability for the receiver achieving the desired state is not deterministic, i.e., \(P^{N>2}_{suc}<1\), for N > 2 preparers in the second protocol. Through constructing two sets of adaptive projective measurement bases for both the real space and the complex space, an improved deterministic N-to-one JRSP protocol for an arbitrary single-qubit state is presented. Analysis shows our protocol can truly achieve the unit success probability, i.e., \(P^{N\geq 2}_{suc}=1\). What is more, the receiver can be randomly assigned even after the distribution of the qubits of EPR pairs, so it is more flexible and applicable in the network situation.