In the last years, Internet of Things (IoT) grew up in an exponential behavior and required long range and low power wireless transmissions. Several standards were proposed and LoRa has emerged as a high potential candidate for many IoT solutions. LoRa modulation is based on a chirp spread-spectrum technique and offers efficient transmission up to 50 kbps over several kilometers. Although the principle is known and studied for decades now, the performance in terms of symbol or bit error probability has been theoretically analyzed in few papers only. Closed-form approximations for additive white Gaussian noise and Rayleigh fading were recently proposed. In this paper, we propose a new approach based on Marcum function. Simulations and comparisons with the state of the art show that the proposed approximation of the Binary Error Probability is up to ten times more accurate for a full SNR range.