Perlin Noise applied to plane, except endpoints

Here goes,

I have created a script that when applied to a plane it creates random hills and valleys as it should. Now here lies my question. How do I make the end points stop at 0 naturally. For example I would have a plane and in the center would be random hills and valleys but the edges would be flat. Here is my Perlin Noise Script;

     public float power = 3.0f;
     public float scale = 1.0f;
     private Vector2 v2SampleStart = new Vector2(0f, 0f);
     
     void Start () 
     {
         Noise ();
     }
     
     void Update () {
         if (Input.GetKeyDown (KeyCode.Space)) 
         {
             v2SampleStart = new Vector2(Random.Range (0.0f, 100.0f), Random.Range (0.0f, 100.0f));
             Noise();
         }
     }
     
     void Noise() {
         MeshFilter mf = GetComponent<MeshFilter>();
         Vector3[] vertices = mf.mesh.vertices;
         for (int i = 0; i < vertices.Length; i++) 
         {    
             float xCoord = v2SampleStart.x + vertices[i].x  * scale;
             float yCoord = v2SampleStart.y + vertices[i].z  * scale;
             vertices[i].y = (Mathf.PerlinNoise (xCoord, yCoord) - 0.5f) * power; 
         }
         mf.mesh.vertices = vertices;
         mf.mesh.RecalculateBounds();
         mf.mesh.RecalculateNormals();
     }

Thanks in advanced!