WaveSpawner

i have a wave spawner script from a video i saw, since I'm fairly new to this still and its just more so a learning experience than anything really, but when spawning in the zombies im quite confused why the Wave Countdown is stuck and not counting down after i have killed them all to go onto another wave? the code for the wavespawner im using is

using UnityEngine; using System.Collections;

public class WaveSpawner : MonoBehaviour {

 public enum SpawnState { SPAWNING, WAITING, COUNTING };

 [System.Serializable]
 public class Wave
 {
     public string name;
     public Transform enemy;
     public int count;
     public float rate;
 }

 public Wave[] waves;
 public int nextWave = 1;
 public int NextWave
 {
     get { return nextWave + 1; }
 }

 public Transform[] spawnPoints;

 public float timeBetweenWaves = 5f;
 public float waveCountdown;
 public float WaveCountdown
 {
     get { return waveCountdown; }
 }

 private float searchCountdown = 1f;

 private SpawnState state = SpawnState.COUNTING;
 public SpawnState State
 {
     get { return state; }
 }

 void Start()
 {
     if (spawnPoints.Length == 0)
     {
         Debug.LogError("No spawn points referenced.");
     }

     waveCountdown = timeBetweenWaves;
 }

 void Update()
 {
     if (state == SpawnState.WAITING)
     {
         if (!EnemyIsAlive())
         {
             WaveCompleted();
         }
         else
         {
             return;
         }
     }

     if (waveCountdown <= 1)
     {
         if (state != SpawnState.SPAWNING)
         {
             StartCoroutine( SpawnWave ( waves[nextWave] ) );
         }
     }
     else
     {
         waveCountdown -= Time.deltaTime;
     }
 }

 void WaveCompleted()
 {
     Debug.Log("Wave Completed!");

     state = SpawnState.COUNTING;
     waveCountdown = timeBetweenWaves;

     if (nextWave + 1 > waves.Length - 1)
     {
         nextWave = 0;
         Debug.Log("ALL WAVES COMPLETE! Looping...");
     }
     else
     {
         nextWave++;
     }
 }

 bool EnemyIsAlive()
 {
     searchCountdown -= Time.deltaTime;
     if (searchCountdown <= 0f)
     {
         searchCountdown = 1f;
         if (GameObject.FindGameObjectWithTag("Enemy") == null)
         {
             return false;
         }
     }
     return true;
 }

 IEnumerator SpawnWave(Wave _wave)
 {
     Debug.Log("Spawning Wave: " + _wave.name);
     state = SpawnState.SPAWNING;

     for (int i = 0; i < _wave.count; i++)
     {
         SpawnEnemy(_wave.enemy);
         yield return new WaitForSeconds( 1f/_wave.rate );
     }

     state = SpawnState.WAITING;

     yield break;
 }

 void SpawnEnemy(Transform _enemy)
 {
     Debug.Log("Spawning Enemy: " + _enemy.name);

     Transform _sp = spawnPoints[ Random.Range (0, spawnPoints.Length) ];
     Instantiate(_enemy, _sp.position, _sp.rotation);
 }

}