A novel iterative k-space data-driven technique, namely parallel reconstruction using null operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using singular value decomposition, and an iterative conjugate-gradient approach is proposed to efficiently solve missing k-space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, and stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than generalized autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUNO reconstruction, ultra-high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with eight coils and only a few autocalibration signal lines.