The HF radars of the Super Dual Auroral Radar Network (SuperDARN) provide measurements of the E × B drift of ionospheric plasma over extended regions of the high-latitude ionosphere. With the recent augmentation of the northern hemisphere component to six radars, a sizable fraction of the entire convection zone (approximately one-third) can be imaged nearly instantaneously (∼2 min). To date, the two-dimensional convection velocity has been mapped by combining line-of-sight velocity measurements obtained from pairs of radars within common-volume areas. We describe a new method of deriving large-scale convection maps based on all the available velocity data. The measurements are used to determine a solution for the distribution of electrostatic potential, Φ, expressed as a series expansion in spherical harmonics. The addition of data from a statistical model constrains the solution in regions of no data coverage. For low-order expansions the results provide a gross characterization of the global convection. We discuss the processing of the radar velocity data, the factors that condition the fitting, and the reliability of the results. We present examples of imaging that demonstrate the response of the global convection to variations in the interplanetary magnetic field (IMF). In the case of a sudden polarity change from northward to southward IMF, the convection is seen to reconfigure globally on very short (<6 min) timescales.