Making grid triangular mesh quickly with Numpy

Consider a regular matrix that represents nodes numbered as shown in the figure:

I want to make a list with all the triangles represented in the figure. Which would result in the following 2 dimensional list:[[0,1,4],[1,5,4],[1,2,5],[2,6,5],...,[11,15,14]]

Assuming that the dimensions of the matrix are (NrXNc) ((4X4) in this case), I was able to achieve this result with the following code:

def MakeFaces(Nr,Nc):
    Nfaces=(Nr-1)*(Nc-1)*2
    Faces=np.zeros((Nfaces,3),dtype=np.int32)
    for r in range(Nr-1):
        for c in range(Nc-1):
            fi=(r*(Nc-1)+c)*2
            l1=r*Nc+c
            l2=l1+1
            l3=l1+Nc
            l4=l3+1
            Faces[fi]=[l1,l2,l3]
            Faces[fi+1]=[l2,l4,l3]
    return Faces

However, the double loop operations make this approach quite slow. Is there a way of using numpy in a smart way to do this faster?