Abstract—This paper presents a new upper bound on the endto-end signal-to-noise ratio (SNR) of channel-assisted amplifyand-forward (AF) multi-hop relay networks. The harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining hop SNRs forms the new bound. Closedform expressions are derived for the cumulative distribution function and the moment generating function of this SNR upper bound for independent and non-identically distributed Rayleigh, and independent and identically distributed Nakagami-m fading, where m is an integer. The outage probability and the average symbol error rate bounds are also derived. Our proposed bounds are compared against the existing bounds.