An inherited autosomal dominant trait characterized by abnormally elevated levels of total serum THYROXINE; (T4) in euthyroid patients with abnormal SERUM ALBUMIN that binds T4 with enhanced affinity. The serum levels of free T4, free T3, and TSH are normal. It is one of several T4 abnormalities produced by non-thyroid disorder. This condition is due to mutations of the ALB gene on CHROMOSOME 4.