  Subresultant is a powerful tool for developing various algorithms in computer
algebra. Subresultants for polynomials in standard basis (i.e., power basis)
have been well studied so far. With the popularity of basis-preserving
algorithms, resultants and subresultants in non-standard basis are drawing more
and more attention. In this paper, we develop a formula for B\'ezout
subresultants of univariate polynomials in general basis, which covers a broad
range of non-standard bases. More explicitly, the input polynomials are
provided in a given general basis and the resulting subresultants are
B\'ezout-type expressions in the same basis. It is shown that the subresultants
share the essential properties as the subresultants in standard basis.
