This story is set somewhat after episode 313 "The Firebending Masters." For simplicity, the three other kids that have been with them since the invasion aren't with them anymore.
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"Should we wake them up?" Aang asked his friends.
"No way. It's our day off. They knew we were going to find something fun to do last night. If we don't leave now, we might not make it back before dark. If they want to spend their day off sleeping in, we shouldn't bother them," Toph reasoned. Sokka shrugged, and then he turned away and climbed into Appa's saddle.
"Are we going or what?! Come on!" he said impatiently. Toph climbed up after him; Aang took one last look towards Katara's closed bedroom door and then airbended onto the bison's head.
"Yip yip!" Appa took off and soared away from the Western Air Temple.
In his own bedchamber, Zuko sat up. He had woken right before the Avatar and his friends had started talking about the fact that he and Katara were both still sleeping. Laying down in his bed again, his heart raced as he realized that he was alone with Katara.
He worried a little, too, however -- she had been unnaturally harsh towards him since he had joined their team. Unnatural for her, that is -- he had never thought that the beautiful waterbender who offered to heal his scar would ever be able to giggle so cruelly at him. She was a fierce and powerful fighter, and yet it was her taunting in the calm of everyday life that she was able to hurt him the most.
Too bad I deserve it , he thought as he pulled his clothes on. He silently cursed himself for his actions in the Earth Kingdom; not for the first time, he wished he had listened to his wise uncle when he was around, and hoped that he'd be able to see him again one day.
Exiting his bedchambers, Zuko passed by Katara's still closed door as he headed outside to find breakfast -- or maybe lunch, as the sun was already high in the sky. Was it uncharacteristic of Katara to sleep so late? Zuko wondered as he ate a few pieces of fruit.
A short while later, Katara emerged from the bedroom that she had been sharing with Toph to find herself both well-rested and alone. No, not alone, she realized as she bit into a piece of fruit. She could hear noises in a different area of the temple, not too far away. As she drew nearer, she realized that the noise was coming from the area of the temple they had designated for training sessions. Suddenly she realized that Zuko was firebending, but he wasn't training Aang.
"Where is everybody?" Katara called over, and Zuko stopped his training to look over at her. Her hair was slightly disheveled, but her blue eyes were bright and he thought she looked beautiful. Her tone toward him had not changed, and he knew that he'd have to do something if he ever wanted her to treat him any differently.
"They went out flying. Like they said they would last night, right?" Katara sighed, crossed her arms and looked around. He was sure that she was regretting oversleeping, wishing that she wasn't left alone with him.
"Hey, do you want to fight me?" Zuko asked, bracing himself for a backlash as she threw him a piercing glance, but she responded, "What do you mean, fight you?"
"Well, I've been training for a little while, but there's only so much you get out of it without an opponent. You could spar with me. I'm sure you'd like to take a couple shots at me with that water of yours." He watched her eyes as he said this, hoping for some glimmer of anything less than her unkindness, something that was more like the Katara he almost got to know. She looked away and then quickly looked back with the same fierce glare.
"You're on," she said.
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Katara stood off to the side and did a few stretches and warm up bending moves. She glanced over at him, and saw that he had his back to her and was removing his shirt. As he turned to face her, she couldn't help herself from noticing that he had a nice upper body -- she could sense how strong he was from across the courtyard.
Shaking her head to clear her thoughts, Katara took a stance against the firebender, and prepared to strike.
He made the first move, a jab of fire that she dodged, whirling a water whip out of the pitcher at her hip. He lunged to the side, jabbing and kicking fire at her that she deflected and avoided, all the while launching ice and water attacks at him.
A well-placed ice blast knocked Zuko back a few steps, and as he regained his footing he saw the water in the courtyard fountain growing into the air. He threw his arms up to deflect it, but he was a second too late, and wound up flat on his back soaking wet.
As he got to his feet he saw the smirk on Katara's face. Her eyes told nothing of her feelings toward him, anger or otherwise. All he could see was that she was determined and passionate, a look that he'd seen many times since he'd begun hunting the Avatar -- it was the look she got whenever she protected her friends, whenever she fought for anything. He admired her for that, and found his courage as he looked into her own fearless eyes.
Zuko took a few steps closer to Katara, and she backed away, closer to the wall of the temple. His entire body was heating up, and he held a flame in each hand. Katara threw ice daggers at him, which melted to quickly to do any harm. As he grew closer, she drew up a large shield of ice to protect her, but the heat he was radiating allowed him to walk straight threw it.
Suddenly he was right in front of her, and his fire had gone out, and he had grabbed her arms and pinned her to the wall of the temple -- it happened so quickly, she had no time to react and was shocked to find his hands pressing her to the stone. She noticed that yes, he was quite strong, and she found herself looking into his eyes, fiery gold and full of passion, and he was staring back at her.