Joint extraction of entities and relations from unstructured text is a crucial task in the construction of knowledge graph and natural language processing. Current methods simplify the implementation by breaking down joint extraction into modular stages. Despite their substantial performance, limitations such as cascading errors and redundancy in relational predictions persist. These issues arise from the oversight of the interdependence and inseparability of the three elements in a triple. In order to tackle these challenges, we introduce a novel Fine-Grained Triplet Classification Model(FTC) that relies on a score-based classifier and a tagging strategy for relation-specific upper triangular. The classifier evaluates if a token pair and relation form a factual triple, while the tagging strategy ensures straightforward and efficient decoding. In comprehensive experiments on four well-established datasets for relation triple extraction, FTC outperforms state-of-the-art baselines, consistently achieving performance improvements across diverse overlapping patterns and complex scenarios involving multiple triples. Our approach acknowledges the interconnected nature of entities and relations, mitigating cascading errors and reducing redundancy in predictions. Through this innovative perspective, the FTC demonstrates its effectiveness in enhancing the accuracy and efficiency of joint entity and relation extraction from unstructured text.