We present a new algorithm for radiative transfer, based on a statistical Monte-Carlo approach, that does not suffer from teleportation effects on the one hand, and yields smooth results on the other hand. Implicit-Monte-Carlo (IMC) techniques for modeling radiative transfer exist from the 70s. However, in optically thick problems, the basic algorithm suffers from `teleportation errors, where the photons propagate faster than the exact physical behavior, due to the absorption-black body emission processes. One possible solution is to use semi-analog Monte-Carlo, in its new implicit form (ISMC), that uses two kinds of particles, photons and discrete material particles. This algorithm yields excellent teleportation-free results, however, it also results with nosier solutions (relative to classic IMC) due to its discrete nature. Here, we derive a new Monte-Carlo algorithm, Discrete implicit Monte-Carlo (DIMC) that uses the idea of the two-kind discrete particles and thus, does not suffer from teleportation errors. DIMC implements the IMC discretization and creates new radiation photons each time step, unlike ISMC. This yields smooth results as classic IMC, due to the continuous absorption technique. One of the main parts of the algorithm is the avoidance of population explosion of particles, using particle merging. We test the new algorithm in both one and two-dimensional cylindrical problems, and show that it yields smooth, teleportation-free results. We finish in demonstrating the power of the new algorithm in a classic radiative hydrodynamic problem, an opaque radiative shock wave. This demonstrates the power of the new algorithm in astrophysical scenarios.
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