algorithm - Diamond-square terrain generation problem

I've implemented a diamond-square algorithm according to this article: http://www.lighthouse3d.com/opengl/terrain/index.php?mpd2

The problem is that I get these steep cliffs all over the map. It happens on the edges, when the terrain is recursively subdivided:

Here is the source:

void DiamondSquare(unsigned x1,unsigned y1,unsigned x2,unsigned y2,float range)
    {      
    int c1 = (int)x2 - (int)x1;
    int c2 = (int)y2 - (int)y1;
    unsigned hx = (x2 - x1)/2;
    unsigned hy = (y2 - y1)/2;
    if((c1 <= 1) || (c2 <= 1))
            return;

// Diamond stage

float a = m_heightmap[x1][y1];
float b = m_heightmap[x2][y1];
float c = m_heightmap[x1][y2];
float d = m_heightmap[x2][y2];
float e = (a+b+c+d) / 4 + GetRnd() * range;

m_heightmap[x1 + hx][y1 + hy] = e;

// Square stage
float f = (a + c + e + e) / 4 + GetRnd() * range;

m_heightmap[x1][y1+hy] = f;
float g = (a + b + e + e) / 4 + GetRnd() * range;
m_heightmap[x1+hx][y1] = g;
float h = (b + d + e + e) / 4 + GetRnd() * range;
m_heightmap[x2][y1+hy] = h;
float i = (c + d + e + e) / 4 + GetRnd() * range;
m_heightmap[x1+hx][y2] = i;

DiamondSquare(x1, y1, x1+hx, y1+hy, range / 2.0);   // Upper left
DiamondSquare(x1+hx, y1, x2, y1+hy, range / 2.0);   // Upper right

DiamondSquare(x1, y1+hy, x1+hx, y2, range / 2.0);   // Lower left
DiamondSquare(x1+hx, y1+hy, x2, y2, range / 2.0);       // Lower right

}

Parameters: (x1,y1),(x2,y2) - coordinates that define a region on a heightmap (default (0,0)(128,128)). range - basically max. height. (default 32)

Help would be greatly appreciated.