The paper describes a near-maximum-likelihood detection process suitable for use in a synchronous serial digital data transmission system that operates at 9600 bit/s over an HF radio link. The data signal at the input and output of the HF radio link is here a 2400 baud 16-level QAM signal with a bandwidth (measured between the 6 dB points) from about 600 to 3000 Hz. The detector is a development of a technique that operates at 2400 bit/s with a four-level QAM signal and which itself originated from a reduced-state Viterbialgorithm detector. Results of computer simulation tests are presented, showing the tolerance to additive white Gaussian noise of a 9600 bit/s data transmission system employing the new detector and operating over a model of an HF radio link. The latter has two independent Rayleigh fading sky waves that introduce frequency spreads of 0.5 or 2 Hz into the data signal and have a relative transmission delay of 1 or 3 ms. It is assumed that the correct estimation of the channel is achieved at the receiver. List of principal symbols = component of the cost d k of a vector P k (eqns. 26-28) = component of the cost d' k of a vector P k (eqns. 30-32) = cost of vector P k (eqn. 29) = alternative cost of vector P k (eqn. 33) e(k) flf+1 j m n Q k T = location of component of Y k+f{k) with the greatest absolute value, over the first f(k) components (eqn. 21 and expr. 22) = location of first significant component of Y k+f{k) (eqn. 21 and expr. 22) = number of components of Y { (eqn. 3)