How can I prevent my player to fly up when my mouse look up>?

Everytime I use the mouse look script and I look up at the sky and move forward it always make my player fly up. How can I stop that from happening. This is the script

using UnityEngine;
using System.Collections;

/// MouseLook rotates the transform based on the mouse delta.
/// Minimum and Maximum values can be used to constrain the possible rotation

/// To make an FPS style character:
/// - Create a capsule.
/// - Add a rigid body to the capsule
/// - Add the MouseLook script to the capsule.
///   -> Set the mouse look to use LookX. (You want to only turn character but not tilt it)
/// - Add FPSWalker script to the capsule

/// - Create a camera. Make the camera a child of the capsule. Reset it's transform.
/// - Add a MouseLook script to the camera.
///   -> Set the mouse look to use LookY. (You want the camera to tilt up and down like a head. The character already turns.)
[AddComponentMenu("Camera-Control/Mouse Look")]
public class MouseLook : MonoBehaviour {

	public enum RotationAxes { MouseXAndY = 0, MouseX = 1, MouseY = 2 }
	public RotationAxes axes = RotationAxes.MouseXAndY;

	public float sensitivityX = 15F;
	public float sensitivityY = 15F;

	public float minimumX = -360F;
	public float maximumX = 360F;

	public float minimumY = -60F;
	public float maximumY = 60F;

    public float moveSensitivity = 1.0f;

	float rotationX = 0F;
	float rotationY = 0F;

	Quaternion originalRotation;

	void Update ()
	{
        //if (Input.GetMouseButton(0))
        //{
            if (axes == RotationAxes.MouseXAndY)
            {
                // Read the mouse input axis
                rotationX += Input.GetAxis("Mouse X") * sensitivityX;
                rotationY += Input.GetAxis("Mouse Y") * sensitivityY;

                rotationX = ClampAngle(rotationX, minimumX, maximumX);
                rotationY = ClampAngle(rotationY, minimumY, maximumY);

                Quaternion xQuaternion = Quaternion.AngleAxis(rotationX, Vector3.up);
                Quaternion yQuaternion = Quaternion.AngleAxis(rotationY, Vector3.left);

                transform.localRotation = originalRotation * xQuaternion * yQuaternion;
            }
            else if (axes == RotationAxes.MouseX)
            {
                rotationX += Input.GetAxis("Mouse X") * sensitivityX;
                rotationX = ClampAngle(rotationX, minimumX, maximumX);

                Quaternion xQuaternion = Quaternion.AngleAxis(rotationX, Vector3.up);
                transform.localRotation = originalRotation * xQuaternion;
            }
            else
            {
                rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
                rotationY = ClampAngle(rotationY, minimumY, maximumY);

                Quaternion yQuaternion = Quaternion.AngleAxis(rotationY, Vector3.left);
                transform.localRotation = originalRotation * yQuaternion;
            }
        //}

        /*Vector3 moveVector = new Vector3(0, 0, 0);
        if (Input.GetKey(KeyCode.D)) moveVector.x += moveSensitivity;
        if (Input.GetKey(KeyCode.A)) moveVector.x -= moveSensitivity;
        if (Input.GetKey(KeyCode.W)) moveVector.z += moveSensitivity;
        if (Input.GetKey(KeyCode.S)) moveVector.z -= moveSensitivity;

        transform.localPosition += transform.TransformDirection( moveVector );*/
	}
	
	void Start ()
	{
		// Make the rigid body not change rotation
		if (rigidbody)
			rigidbody.freezeRotation = true;
		originalRotation = transform.localRotation;
	}
	
	public static float ClampAngle (float angle, float min, float max)
	{
		if (angle < -360F)
			angle += 360F;
		if (angle > 360F)
			angle -= 360F;
		return Mathf.Clamp (angle, min, max);
	}
}

You’ve commented out all the movement code. Uncomment this code and then replace line 81 with the following three lines (untested):

    Vector3 v3 = transform.TransformDirection( moveVector );
    v3.y = 0;
    transform.localPosition += v3;

P.S. You may want to use ‘transform.position’ instead of ‘transform.localPosition’. I’m not sure why this code is using ‘localPosition’.