This paper presents a new procedure for the automated estimation of the phase relation between thoracic and abdominal breathing signals measured by inductance plethysmography (RIP). This estimation is achieved using linear filters, binary converters and an exclusive-or gate. The filters are designed offline from prior knowledge of the spectrum of subjects' respiration, reducing computational complexity and providing on-line processing capabilities. Some numerical results based on simulated time series and infant respiration data are provided, showing that the new method is less biased than the Pearson correlation method, commonly used for assessment of thoracoabdominal asynchrony. Our method offers further advantages: 1) it works with uncalibrated measurements; 2) it provides quantitative phase estimates with no need to estimate the underlying frequency of the breathing signals; 3) it does not require nonconvex optimization search algorithms; and 4) it is easy to implement and to automate.