Abstract: Firstly, the concept of cardinal multiwavelets is given. In addition, the properties of this kind of multiwavelets are investigated. And the sufficient and necessary conditions for multiwavelets with general cardinal and orthogonal properties and those with general cardinal and symmetric properties are establisbed, which can overcome the shortcoming of the present sampling theorem for multiwavelets: there is no multiwavelets with cardinal and symmetric properties simultaneously until now. Secondly, since the construction of multiwavelets with some specified property requires the solution of a large and complex system of nonlinear design equations, Hopfield feedback neural networks are used instead of using software Singular, which is in most common use at present, to construct the multiwavelets. The experiments show that the method can not only offer the satisfactory solutions when the proper initial values are chosen, but also overcome the mass time-cost by using Singular to carry out the Grbner basis computations.