Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u t =–A2 u. Using a representation of the semi group exp(–A2 t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w t = w yy , with initial values v solving the initial value problem for v y = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2nd order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4th order equation for u to that of the 2nd order equation for v, followed by the solution of the heat equation in one space variable.