The solution of many important signal processing problems depends on the estimation of the parameters of a Hidden Markov Model (HMM). Unfortunately, to date the only known methods for performing this estimation have been iterative, and therefore computationally demanding. By way of contrast, this paper presents a new fast and non-iterative method that utilizes certain recent `state spaced subspace system identification' (4SID) ideas from the control theory literature. A short simulation example presented here indicates this new technique to be almost as accurate as Maximum-Likelihood estimation, but an order of magnitude less computationally demanding than the Baum--Welch (EM) algorithm.