Was Lord Shiva justified in killing Yama?

[It is said that Lord Shiva killed the Lord of Death, Yama, who was doing his duty by taking the life of Markandeya? Is this justified?]

When the story of Markandeya is read, it looks as if Lord Shiva was conquered by His anger and killed Yama, who only an officer doing his duty. Lord Shiva killed Yama because His devotee, Markandeya, was affected. This breaks the rule of Karma, which was established by the Lord Himself. Latter on when all the angels prayed Lord Shiva realized His mistake and gave life to Yama. This story tarnishes the divine personality of the Lord. It looks as if the Lord acted in haste and anger. Later on when some other person who is wise advised the Lord, the Lord rectified His mistake. The background of this story is not linked. Actually Yama gave the life to Satyavaan when his wife Savitri praised him. Then Yama violated his duty. But when Markandeya is praising Lord Shiva, Yama insisted about his duty. Therefore Lord Shiva taught a lesson. If Yama was impartial in the case of Savithri, the Lord would have not interfered in the duty of Yama. When the back ground is realized the divine personality of Lord Shiva was very much enlightened. Only to teach Yama, Lord Shiva gave Markandeya as the son to Mrukandu. Markandeya was the incarnation of radiation of Lord Shiva. The story of Markandeya was created by Lord Shiva only to teach Yama.