A least squares procedure called GIPSCAL (a Generalized Inner Product multidimensional SCALing) is proposed which extends Chino's ASYMSCAL into higher dimensions than three. GIPSCAL fits the inner product of two vectors and the area of the parallelogram spanned by these vectors, respectively, for the symmetric and skew-symmetric parts of observed similarity judgements. It is shown that GIPSCAL has a very desirable property that the geometrical interpretation of asymmetric parts in similarity judgements is reducible to that of the area of the parallelogram spanned by vectors in two dimensions. It is also shown that GIPSCAL permits a social psychological justification for the cause of asymmetry. Relation to distance model is discussed. Examples of application are given to demonstrate the feasibility of the model.