We present in this paper an algebraic derivative method of the line current in order to detect the presence of series arcs in an AC or DC electrical installation. The first derivative is computed from a limited Taylor-McLaurin series transposed in Laplace space. The temporal estimation is achieved by integration over a sliding window of the product of a particular polynomial with the instantaneous current. The discrete version can be synthesized by a simple FIR filter. The tests, with and without series arc, are conducted on experimental currents (3-12 A) measured on domestic loads (resistors, vacuum drill, dimmer). The sampling frequency is set to 1 MHz. Short integration times (50 μs in AC and 200 μs in DC) are sufficient to observe, with high contrast, the derivative peaks due to the arc ignition. The detection is then performed by comparing the derivation filter output to its instantaneous noise level. The response time is equal to the integration duration. This method, simple to set up and easy to implement, is ideally suited for installations that do not use load switching current.