I will present an algorithm that, for a given vector of n relatively prime polynomials in one variable over an arbitrary field, outputs an invertible matrix with polynomial entries such that it forms a degree-optimal moving frame for the rational curve defined by the input vector. From an algebraic point of view, the first column of the matrix consists of a minimal-degree Bezout vector (a minimal-degree solution to the univariate effective Nullstellensatz problem) of the input vector, and the last n-1 columns comprise an optimal-degree basis, called a mu-basis, of the syzygy module of the input vector. The algorithm and underlying theory are based on elementary linear algebra and will be accessible to all. This is a joint work with Drs. Hoon Hong and Irina Kogan.