It is proposed that the tidal input functions and observed tide be represented as linear combinations of a set of special orthogonal tidal functions, referred to as orthotides. These functions differ from the usual harmonic functions in that successive members represent successively more wiggliness in the linear admittance function. The tidal constants appropriate to this scheme are determined from the mean displaced products of the observed tide with the tidal input functions, as is done in the convolution method. Mean displaced products and linear orthotides were computed for the semidiurnal and diurnal gravitational tidal inputs. Results of Munk and Cartwright's analysis of 19 years of observed data from Honolulu, Hawaii, and Newlyn, England, were used to estimate the linear gravitational orthotide constants for those two places. The general decrease of magnitude with order of the estimated orthotide constants indicates that the tidal admittance is relatively smooth, as is expected. A procedure is outlined for a similar development of the bilinear tidal response. It is suggested that this orthogonal method be used for the routine analysis and prediction of tides, as it is more readily standardized and systematized than methods heretofore used.