Trying to get a smooth gridmove

I'm using a modified gridmove script thats on the wiki. The exact code is below. The issues I have is when I'm holding down the arrow keys, the movement isn't smooth. Its like it pauses a fraction of a second on each grid before moving to the next location. It seems as though there is a curve to the speed from grid to grid location, starts slow, speeds up, slows down, pauses 200ms and then moves on.

How can I get smooth movement when the arrow keys are pressed, but still limit the movement to a grid?

 using System.Collections;
 using UnityEngine;
 
 class GridMove : MonoBehaviour {
     private float moveSpeed = 4f;
     private float gridSize = 1f;
     private enum Orientation {
         Horizontal,
         Vertical
     };
     private Orientation gridOrientation = Orientation.Horizontal;
     private bool allowDiagonals = false;
     private bool correctDiagonalSpeed = true;
     private Vector2 input;
     private bool isMoving = false;
     private Vector3 startPosition;
     private Vector3 endPosition;
     private float t;
     private float factor;
     private string lastDirection = "";
 
     public void Update() {
         if (!isMoving) {
             input = new Vector2(Input.GetAxis("Horizontal"), Input.GetAxis("Vertical"));
             if (!allowDiagonals) {
                 if (Mathf.Abs(input.x) > Mathf.Abs(input.y)) {
                     input.y = 0;
                 } else {
                     input.x = 0;
                 }
             }
 
             string direction = "none";
             if (input.x > 0 && input.y == 0) {
                 direction = "right";
             }
             else if (input.x < 0 && input.y == 0) {
                 direction = "left";
             }
             else if (input.x == 0 && input.y > 0) {
                 direction = "up";
             }
             else if (input.x == 0 && input.y < 0) {
                 direction = "down";
             }
             if (!lastDirection.Equals(direction)) {
                 Messenger.Broadcast<GameObject, string>("PlayerDirection", transform.gameObject, direction);
                 lastDirection = direction;
             }
 
             if (input != Vector2.zero) {
                 StartCoroutine(move(transform));
             }
         }
     }
     
     public IEnumerator move(Transform transform) {
         isMoving = true;
         t = 0;
 
         if (startPosition == endPosition) {
             startPosition = transform.position;
             if(gridOrientation == Orientation.Horizontal) {
                 endPosition = new Vector3(startPosition.x + System.Math.Sign(input.x) * gridSize,
                                           startPosition.y, startPosition.z + System.Math.Sign(input.y) * gridSize);
             } else {
                 endPosition = new Vector3(startPosition.x + System.Math.Sign(input.x) * gridSize,
                                           startPosition.y + System.Math.Sign(input.y) * gridSize, startPosition.z);
             }
         }
 
         RaycastHit hitInfo;
         if (Physics.Linecast(startPosition, endPosition, out hitInfo)) {
             if (hitInfo.transform.tag.Equals("NO_PASS") || hitInfo.transform.tag.Equals("ROCK")) {
                 endPosition = startPosition;
             }
             Messenger.Broadcast<GameObject>("PlayerEat", hitInfo.transform.gameObject);
         }
 
         if(allowDiagonals && correctDiagonalSpeed && input.x != 0 && input.y != 0) {
             factor = 0.7071f;
         } else {
             factor = 1f;
         }
         
         while (t < 1f) {
             t += Time.deltaTime * (moveSpeed/gridSize) * factor;
             if (t > 1.0) {
                 t = 1.0f;
             }
             transform.position = Vector3.Lerp(startPosition, endPosition, t);
             yield return null;
         }
 
         startPosition = endPosition;
         isMoving = false;
         yield return 0;
     }
 }