The FatBear filter is a nonarithmetic filter for piecewise constant signals in high noise situations. The output of each window takes the pseudo-median of the medians of all sets of N + 1 values with minimum range. The Recursive FatBear filter is the extension of the FatBear filter. It replaces the original signal with the output before shifting the window to the next position. In this paper, we study the properties of the Recursive FatBear filter for pulse width filtering, impulse rejection, and edge enhancement. Experimental examples show that the Recursive FatBear filter is more effective than the FatBear filter in eliminating white Gaussian noise when the signal-to-noise ratio is large and still enhancing the edge. The fixed points of the FatBear filter are shown to also be fixed points of the Recursive FatBear filter. In addition a 2-D hybrid MED-Fatbear filter is presented and theoretical results for the recursive and nonrecursive case are presented for the 2-D case. Applications to synthetic data and to real images are given.