This paper presents a new imaging method, applicable for both 2D and 3D imaging. It is based on Synthetic Transmit Aperture Focusing, but unlike previous approaches a new frame is created after every pulse emission. The elements from a linear transducer array emit pulses one after another. The same transducer element is used after N-xmt emissions. For each emission the signals from the individual elements are beam-formed in parallel for all directions in the image. A new frame is created by adding the new RF lines to the RF lines from the previous frame. The RF data recorded at the previous emission with the same element are subtracted. This yields a new image after each pulse emission and can give a frame rate of e.g. 5000 images/sec.<br/><br/>The paper gives a derivation of the recursive imaging technique and compares simulations for fast B-mode imaging with measurements.<br/><br/>A low value of N-xmt is necessary to decrease the motion artifacts and to make flow estimation possible. The simulations show that for N-xmt = 13 the level of grating lobes is less than -50 dB from the peak, which is sufficient for B-mode imaging and flow estimation.<br/><br/>The measurements made with an off-line experimental system having 64 transmitting channels and 1 receiving channel, confirmed the simulation results. A linear array with a pitch of 208.5 mu m, central frequency f(0tr) = 7.5 MHz and bandwidth BW = 70% was used. The signals from 64 elements were recorded, beam-formed and displayed as a sequence of B-mode frames, using the recursive algorithm. An excitation with a central frequency f(0) = 5 MHz (lambda = 297 mu m in water) was used to obtain the point spread function of the system. The -6 dB width of the PSF is 1.056 mm at axial distance of 39 mm. For a sparse synthetic transmit array with N-xmt = 22 the expected grating lobes from the simulations are -53 dB down from the peak value at, positioned at +/-28 degrees. The measured level was -51 dB at +/-27 degrees from the peak.<br/><br/>Images obtained with the experimental system are compared to the simulation results for different sparse arrays. The application of the method for 3D real-time imaging and blood-velocity estimations is discussed.