We propose a concept for rapid generation of tunable, shear-free, mobile gradients in open space which we define as floating gradient. A microfluidic probe with 4 apertures arranged at the corners of a virtual square, two for injecting fluids and two for aspiration. The simultaneous injection from two apertures results to a head-to-head flow at the center of the MFP, and the formation of a stagnation point, while aspiration by the two other apertures results in hydrodynam-ic confinement of the injected streams, forming a quadrupole-like microfluidic field. The two injected streams are the source and sink, respectively, and a gradient is formed across the shear-free, stagnation point. We show that the gradient is formed rapidly, can be tuned by changing the aspiration flow rate, and can be moved either hydrodynamically by changing the flow ratio between the two aspiration apertures and/or two injection apertures, or can be moved by physically displacing the microfluidic probe. We expect the floating gradient concept to be useful for surface patterning and cell studies.