Keeping the character's speed the same

So I’m trying to create a Dota or LoL type movement(which I am oh so very far from doing) and aquired the click to move script from the wiki. I noticed that the farther I click from the character, the faster he will move to it. I want to keep it the same speed no matter how far the mouse’s position is. How do I do this?
Here’s the script:

// Click To Move script

// Moves the object towards the mouse position on left mouse click



var smooth:int; // Determines how quickly object moves towards position



private var targetPosition:Vector3;

var marker : GameObject;

private var mousePos : Vector3;

private var worldPos : Vector3;

var User : GameObject;



function Update () {

 	var controller : CharacterController = GetComponent(CharacterController);

    if(Input.GetKeyDown(KeyCode.Mouse1))

    {         

        var playerPlane = new Plane(Vector3.up, transform.position);

        var ray = Camera.main.ScreenPointToRay (Input.mousePosition);

        var hitdist = 0.0f;

        

        if (playerPlane.Raycast (ray, hitdist)) {

            var targetPoint = ray.GetPoint(hitdist);

            targetPosition = ray.GetPoint(hitdist);

            var targetRotation = Quaternion.LookRotation(targetPoint - transform.position);

            transform.rotation = targetRotation;   
        }
 
       if(Input.GetMouseButton(1)) {

		mousePos = Input.mousePosition;

		mousePos.z = 1;

		var cloneMarker = Instantiate(marker,worldPos,Quaternion.identity);

		Destroy(cloneMarker, .5f);

		}
  
		Debug.DrawLine(User.transform.position, targetPosition, Color.red);
  	

	}

	transform.position = Vector3.Lerp (transform.position, targetPosition, Time.deltaTime * smooth);

}
 
@script RequireComponent(CharacterController)

So, what can i do? Thanks for help!

Remove the easing.
Instead doing “transform.position = Vector3.Lerp (transform.position, targetPosition, Time.deltaTime * smooth);”, do like:

float constantSpeed = 1f;
transform.position = transform.position + (targetPosition - transform.position).normalized * constantSpeed * Time.deltaTime;